Physics 9702 · AS & A Level
Kirchhoff's laws
100 practice questions on Kirchhoff's laws, with worked solutions and instant marking.
There are three cells with e.m.f.s $V_1$, $V_2$ and $V_3$, each with negligible internal resistance. As illustrated, these cells are linked to three resistors of resistance $R_1$, $R_2$ and $R_3$. The current flowing in the circuit is $I$. Which equation is correct?
Feb/March 2016
When obtaining a formula for the total resistance of three resistors connected in series, Kirchhoff’s laws are applied. Which physics principle is used in this derivation?
Feb/March 2016
State Kirchhoff’s second law.
Feb/March 2018
State Kirchhoff’s first law in words.
Feb/March 2021
Kirchhoff’s two laws each assume that a particular quantity is conserved. Which row gives Kirchhoff’s first law and identifies the conserved quantity?
Feb/March 2022
In the circuit diagram, the cells have negligible internal resistance and the galvanometer shows zero. What is the resistance of resistor $R$?
Feb/March 2022
When establishing a formula for the total resistance of three separate resistors connected in series, Kirchhoff’s laws are applied. Which physics principle is used in this derivation?
May/June 2010
Kirchhoff’s laws are applied to derive a formula for the total resistance of three different resistors connected in series. Which physics principle is used in this derivation?
May/June 2010
While obtaining a formula for the total resistance of three different resistors connected in series, Kirchhoff’s laws are applied. Which physics principle is used in this derivation?
May/June 2010
Four resistors with identical resistance are connected as shown. How will the power dissipated by the resistors change when resistor W is removed?
May/June 2011
For a cell, explain what the term electromotive force (e.m.f.) means.
May/June 2011
The diagram represents a circuit that has four voltmeter readings, $V$, $V_1$, $V_2$ and $V_3$. Which equation connecting the voltmeter readings has to be correct?
May/June 2012
State Kirchhoff’s second law.
May/June 2012
State what Kirchhoff’s first law says.
May/June 2012
Which two quantities are linked to the conservation principles behind Kirchhoff’s first and second laws?
May/June 2013
In the circuit diagram shown, every resistor is identical, and the resistance of each ammeter is negligible. Ammeter $A_1$ shows a reading of $0.6\,\text{A}$. What readings do the other ammeters show?
May/June 2014
What is the combined resistance between points $P$ and $Q$ in this resistor network?
May/June 2014
For cell X, the e.m.f. is $2.0\,\text{V}$ and the internal resistance is $2.0\,\Omega$. For cell Y, the e.m.f. is $1.6\,\text{V}$ and the internal resistance is $1.2\,\Omega$. The two cells are connected to a resistor of resistance $0.8\,\Omega$, as illustrated. What is the current in cell X?
May/June 2014
What current flows through the $40\,\Omega$ resistor in the circuit shown?
May/June 2014
Each of Kirchhoff's two laws assumes that one physical quantity remains conserved. Which row gives Kirchhoff's first law and identifies the conserved quantity?
May/June 2015
A cell with e.m.f. $2.0\,\text{V}$ and negligible internal resistance is linked to a resistor network as shown. What is the current $I$?
May/June 2015
A current flows from P to R through the resistor network shown. The potential difference (p.d.) between P and Q is $3\,\text{V}$. The p.d. between Q and R is $6\,\text{V}$. The p.d. between P and S is $5\,\text{V}$. Which row in the table is correct?
May/June 2016
Four resistors are arranged in a square, as illustrated. The resistance can be measured between any pair of junctions. Between which two junctions does the measured resistance have the greatest value?
May/June 2017
A $20\,\text{V}$ d.c. supply is connected to a circuit made up of five resistors $L$, $M$, $N$, $P$ and $Q$. A potential drop of $7\,\text{V}$ occurs across $L$, and there is an additional $4\,\text{V}$ potential drop across $N$. What potential drops are across $M$, $P$ and $Q$?
May/June 2017
At a point in a circuit, the total current entering that point is equal to the total current leaving it. Which statement is correct?
May/June 2018
In the circuit diagram shown, the batteries are assumed to have negligible internal resistance. What are the values of the currents $I_1$, $I_2$ and $I_3$?
May/June 2018
Four distinct resistors are connected in the arrangement shown. A current of $1.5\,\text{A}$ enters the network at junction X and exits at junction Y. What is the current in the resistor with resistance $30\,\Omega$?
May/June 2018
The diagram illustrates a circuit arrangement containing three resistors. Two of them, labelled $R$, are the same. The remaining resistor has a resistance of $5.0\,\Omega$. The resistance between Y and Z is determined to be $2.5\,\Omega$. What is the resistance between X and Y?
May/June 2018
State Kirchhoff’s first law in words.
May/June 2018
A battery with negligible internal resistance is connected to three resistors, as shown. The three resistors all have equal resistance. The current in the battery is $0.30\,\text{A}$. What is the current in resistor X?
May/June 2019
Kirchhoff’s first law says that, at a junction in a circuit, the total current flowing in is the same as the total current flowing out. This law is founded on the conservation of a physical quantity. Which physical quantity is it?
May/June 2019
The arrangement shown uses two cells of electromotive force (e.m.f.) $3.0\,\text{V}$ and $1.2\,\text{V}$, with internal resistance taken as negligible, connected to resistors with resistance $9.0\,\Omega$ and $18\,\Omega$. What is the current $I$ in the $9.0\,\Omega$ resistor?
May/June 2019
State Kirchhoff’s second law in words.
May/June 2019
Kirchhoff’s first and second laws are associated with the conservation of physical quantities. Which quantities do they relate to?
May/June 2020
The circuit shown is supplied by a source with electromotive force (e.m.f.) $V$ and negligible internal resistance. A current of $3.0\,\text{A}$ flows through the $4.0\,\Omega$ resistor. What value does $V$ have?
May/June 2020
A cell with electromotive force (e.m.f.) $E$ and negligible internal resistance is connected into a circuit. As shown, the circuit includes currents $I_1$, $I_2$ and $I_3$, as well as potential differences $V_1$, $V_2$ and $V_3$. Which equation states Kirchhoff's first law?
May/June 2021
The diagram illustrates a circuit in which two batteries are joined together. What is the value of the current $I$?
May/June 2021
A battery with electromotive force (e.m.f.) $E$ and negligible internal resistance is linked to four resistors with resistances $R_1$, $R_2$, $R_3$ and $R_4$. The currents $I_1$ and $I_2$ through the resistors are shown. Which equation is correct?
May/June 2021
State Kirchhoff’s second law for a circuit.
May/June 2021
In an electrical circuit, the total current flowing into a junction is always the same as the total current flowing out of it. Why does this happen?
May/June 2022
Kirchhoff’s first and second laws follow from the conservation of two different quantities. Which quantities are these?
May/June 2022
Which row gives the correct description of Kirchhoff's laws?
May/June 2022
State Kirchhoff’s first law.
May/June 2022
Kirchhoff's first law follows from the conservation of which quantity?
May/June 2023
Each of the three matching cells has electromotive force (e.m.f.) $E$ and negligible internal resistance. The cells are arranged with three matching resistors, each of resistance $R$, as illustrated. What potential difference is across one resistor?
May/June 2023
Kirchhoff’s first law says that, at a junction in a circuit, the total current flowing in is equal to the total current flowing out. This law is founded on the conservation of a physical quantity. What is this physical quantity?
May/June 2023
The circuit shows four resistors, each having resistance $R$. The resistance measured between point X and point Y is $120\,\Omega$ altogether. What is the value of the resistance $R$?
May/June 2024
Which statement correctly describes Kirchhoff’s first law?
May/June 2024
A student assembles the circuit below. The lamps are all identical. Which lamp dissipates the greatest power?
May/June 2024
State Kirchhoff’s first law in words.
May/June 2024
State Kirchhoff’s second law for a closed loop.
May/June 2024
State Kirchhoff’s second law.
May/June 2024
Each of Kirchhoff’s two laws assumes conservation of a quantity. Which row gives Kirchhoff’s first law and identifies the conserved quantity?
May/June 2025
At a point in a circuit, the total of the currents entering it is the same as the total of the currents leaving it. Which statement is correct?
May/June 2025
Each of Kirchhoff’s laws is connected with the conservation of a physical quantity. Which physical quantities are taken to be conserved when formulating Kirchhoff’s first law and Kirchhoff’s second law?
Oct/Nov 2011
The potentiometer circuit shown in Fig. 5.1 is arranged for comparing potential differences. A cell with e.m.f. $E_1$ and internal resistance $r_1$ is placed in series with a resistor of resistance $R_1$ and a uniform metal wire whose total resistance is $R_2$. A second cell with e.m.f. $E_2$ and internal resistance $r_2$ is connected in series with a sensitive ammeter, and this combination is then connected across the wire at $B\,J$. The contact at $J$ lies halfway along the wire. The directions of the currents are indicated in Fig. 5.1.
Oct/Nov 2011
Distinguish between potential difference (p.d.) and electromotive force (e.m.f.) by referring to the energy transformations involved.
Oct/Nov 2011
The diagram presents a four-terminal box linked to a battery and two ammeters. The readings on the two meters are the same. Which circuit inside the box will produce this outcome?
Oct/Nov 2012
The diagram illustrates a resistor network. The potential difference across the network is $V$. Is the equation shown below valid for the network? $V = I\left(\frac{1}{R_1} + \frac{1}{R_2} + R_3\right)$
Oct/Nov 2012
In Fig. 5.1, a $12\,\text{V}$ power supply with negligible internal resistance is connected to a uniform metal wire AB. This wire is $1.00\,\text{m}$ long and has resistance $10\,\Omega$. A $4.0\,\Omega$ resistor and a $2.0\,\Omega$ resistor are joined in series across the wire. The currents $I_1$, $I_2$ and $I_3$ are labelled as in Fig. 5.1.
Oct/Nov 2012
Figure 4.1 shows a circuit arranged to measure the power transferred from a battery. The power is delivered to a variable resistor with resistance $R$. The battery has an electromotive force (e.m.f.) $E$ and an internal resistance $r$. Across $R$ there is a potential difference (p.d.) $V$. The current in the circuit is $I$.
Oct/Nov 2012
Four resistors with resistances $R$, $2R$, $3R$ and $4R$ are arranged to make a network. As shown, a battery with negligible internal resistance and a voltmeter are connected to the resistor network. The voltmeter shows a reading of $2\,\text{V}$. Find the electromotive force (e.m.f.) of the battery.
Oct/Nov 2013
A $20\,\text{V}$ d.c. power supply is connected to a circuit made up of five resistors L, M, N, P and Q. Across L there is a potential drop of $7\,\text{V}$, and across N there is an additional potential drop of $4\,\text{V}$. What are the potential drops across M, P and Q?
Oct/Nov 2013
For two resistors with resistances $R_1$ and $R_2$ connected in parallel, the total resistance $R_T$ is given by the formula shown below. $$\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2}$$ Which statement is used to derive this formula?
Oct/Nov 2014
A battery with electromotive force (e.m.f.) $12\,\text{V}$ and internal resistance $r$ is joined in series to two resistors, each of fixed resistance $X$, as shown in Fig. 5.1. The current $I_1$ delivered by the battery is $1.2\,\text{A}$. The same battery is then connected to the same two resistors in parallel, as shown in Fig. 5.2. The current $I_2$ delivered by the battery is $3.0\,\text{A}$.
Oct/Nov 2014
The diagram represents a four-terminal box linked to a battery and two ammeters. The readings on the two meters are the same. Which circuit inside the box would produce this outcome?
Oct/Nov 2015
An arrangement of resistors, each having resistance $1\,\Omega$, is joined as illustrated. The current in the resistor at the far end is $1\,\text{A}$. What is the potential difference (p.d.) $V$ between the input terminals?
Oct/Nov 2015
In the circuit diagram, the ammeter gives a zero reading. The four resistors are of different resistance values $R_1$, $R_2$, $R_3$ and $R_4$. Which equation is correct?
Oct/Nov 2016
In the circuit diagram, currents $I_1$, $I_2$, $I_3$, $I_4$ and $I_5$ are shown in different branches. Which equation is correct?
Oct/Nov 2016
For the circuit illustrated, a current of $3.0\,\text{A}$ flows through the $2.0\,\Omega$ resistor. Determine the current $I$ supplied by the power supply and the voltage $V$ across it.
Oct/Nov 2016
In the diagram, the currents $I_1$, $I_2$, $I_3$, $I_4$ and $I_5$ are shown in separate branches of a circuit. Which equation is the correct one?
Oct/Nov 2016
State Kirchhoff’s second law for a circuit.
Oct/Nov 2016
A cell with electromotive force $E$ and negligible internal resistance is joined to a resistor network containing resistances $R_1$, $R_2$, $R_3$ and $R_4$, as illustrated. The circuit branches carry currents $I_1$, $I_2$ and $I_3$. Which equation is correct?
Oct/Nov 2017
In the circuit diagram, the resistor $S$ is connected so that it is neither in series with nor in parallel to the other resistors. Using Kirchhoff’s laws together with the information given in the diagram, it is possible to work out the resistance of each of the two identical resistors marked $R$. What is the resistance of each resistor $R$?
Oct/Nov 2017
A resistor $R$ is joined in series with two cells, each of electromotive force (e.m.f.) $E$ but with different internal resistances $r_1$ and $r_2$. The voltmeter reading is $0\,\text{V}$. What is the resistance of $R$?
Oct/Nov 2017
There are three identical cells, each with electromotive force (e.m.f.) $E$ and negligible internal resistance. As shown, the cells are linked to three identical resistors, each of resistance $R$. What potential difference is there between P and Q?
Oct/Nov 2017
Three cells with electromotive forces (e.m.f.) $E_1$, $E_2$ and $E_3$ are arranged in the circuit shown in Fig. 5.1. The circuit also contains resistors with resistances $R_1$, $R_2$, $R_3$ and $R_4$. The currents in the separate branches are $I_1$, $I_2$ and $I_3$. The cells have negligible internal resistance.
Oct/Nov 2017
A battery is attached to a circuit made up of six resistors, as shown. The potential differences across five of the resistors are marked on the diagram. What is the potential difference across resistor $R$?
Oct/Nov 2018
Kirchhoff’s second law is derived from a fundamental principle. Which principle is this?
Oct/Nov 2018
For the circuit diagram shown, the ammeter has a reading of zero. What is the resistance of resistor R?
Oct/Nov 2018
State Kirchhoff’s second law.
Oct/Nov 2018
Kirchhoff’s two laws for electric circuits can be obtained by applying conservation laws. Which conservation laws form the basis of Kirchhoff’s laws?
Oct/Nov 2019
The diagram illustrates a circuit that has four voltmeters. Their readings are $V_1$, $V_2$, $V_3$ and $V_4$. Every reading is positive. Which equation linking the voltmeter readings is correct?
Oct/Nov 2019
In the circuit diagram, every resistor is identical and each ammeter has negligible resistance. The reading $A_1$ is $0.6\,\text{A}$. What readings do the other ammeters show?
Oct/Nov 2019
Two cells, with electromotive forces $E_1$ and $E_2$ and internal resistances $r_1$ and $r_2$, are connected to a resistor $R$ as shown. The terminal potential difference across cell 1 is zero. Which expression gives the resistance of resistor $R$?
Oct/Nov 2019
Which row gives the correct description of Kirchhoff’s laws?
Oct/Nov 2019
State what Kirchhoff’s first law says.
Oct/Nov 2019
A battery with electromotive force (e.m.f.) $12\,\text{V}$ and negligible internal resistance is linked to a circuit containing two lamps and two resistors, as illustrated in Fig. 6.1. The two lamps in the circuit have the same resistance. The two resistors have resistances $R$ and $28\,\Omega$. The lamps are joined at junction X and the resistors are joined at junction Y. The current in the battery is $0.50\,\text{A}$ and the current in the lamps is $0.20\,\text{A}$.
Oct/Nov 2019
The circuit shows three identical cells, each with electromotive force (e.m.f.) $E$ and internal resistance $r$. What potential difference exists between points X and Y?
Oct/Nov 2021
A battery with negligible internal resistance is linked to three resistors, as illustrated. The potential difference across every resistor is $2\,\text{V}$. The current supplied by the battery is $0.4\,\text{A}$, and the current through one of the resistors in parallel is $0.3\,\text{A}$. What is the current through the other resistor in parallel, and what is the electromotive force (e.m.f.) of the battery?
Oct/Nov 2021
State Kirchhoff’s first law in words.
Oct/Nov 2021
Each of Kirchhoff’s laws is associated with the conservation of a physical quantity. Which conserved physical quantities are applied when deriving Kirchhoff’s first law and Kirchhoff’s second law?
Oct/Nov 2022
In the circuit $PQR$ shown, three batteries and three identical resistors are connected together. The batteries have negligible internal resistance. What is the potential difference between points $P$ and $Q$?
Oct/Nov 2022
State what Kirchhoff’s second law says.
Oct/Nov 2022
Kirchhoff’s first and second laws arise from the conservation of which quantities?
Oct/Nov 2023
Kirchhoff's first law follows from conservation of which physical quantity?
Oct/Nov 2023
The diagram represents a resistor network. Every resistor has a resistance of $6.0\,\Omega$. What is the total resistance of the network between points $X$ and $Y$?
Oct/Nov 2023
Three resistors, $R_1$, $R_2$ and $R_3$, are joined in parallel to a cell. The currents through the resistors are $I_1$, $I_2$ and $I_3$. The p.d.s across the resistors are $V_1$, $V_2$ and $V_3$. The current in the cell is $I_0$. The p.d. across the cell is $V_0$, as shown. Which equation can be deduced by applying Kirchhoff's second law to the circuit?
Oct/Nov 2023
Kirchhoff’s second law follows from a fundamental principle. What is that principle?
Oct/Nov 2024
Each of Kirchhoff’s laws expresses a conservation principle for a physical quantity. Which quantity is conserved by each law?
Oct/Nov 2024