Physics 9702 · AS & A Level · Capacitors and capacitance

Capacitors and capacitance — practice question

(a)[1]

Define capacitance in words.

(b(i))[1]

An isolated metal sphere of radius $r$ is charged so that its potential is $V$ and the charge on it is $q$. The charge can be treated as if it were a point charge at the centre of the sphere. State an expression, in terms of $r$ and $q$, for the sphere’s potential $V$.

(b(ii))[1]

This isolated sphere has capacitance. Use your answers in (a) and (b)(i) to show that the capacitance of the sphere is proportional to its radius.

(c(i))[3]

The sphere in (b) has a capacitance of $6.8 \, \text{pF}$ and is charged to a potential of $220 \, \text{V}$. Calculate the radius of the sphere.

(b)

An isolated metal sphere of radius $r$ is charged so that its potential is $V$ and the charge on it is $q$. The charge can be treated as if it were a point charge at the centre of the sphere.

(c)

The sphere in (b) has a capacitance of $6.8\,\text{pF}$ and is charged to a potential of $220\,\text{V}$. Calculate

(c(ii))[1]

the charge, in coulomb, on the sphere.

(d)

A second uncharged metal sphere is brought up to the sphere in (c) so that they touch. The combined capacitance of the two spheres is $18\,\text{pF}$. Calculate

(d(i))[1]

the potential of the two spheres.

(d(ii))[3]

the change in the total energy stored on the spheres when they touch.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: charge per unit potential difference

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