State, with reference to the power dissipated in a resistor, the meaning of the root-mean-square (r.m.s.) value of an alternating voltage.
A coil turns freely on frictionless bearings at constant speed in a uniform magnetic field. As it turns, an induced alternating electromotive force (e.m.f.) appears across the open terminals of the coil. The induced e.m.f. has r.m.s. value $12\,\text{V}$ and frequency $50\,\text{Hz}$. The rotational speed of the coil is now doubled.
State and explain, with reference to the principles of electromagnetic induction, what effect the increased rotational speed has on the r.m.s. value of the induced e.m.f.
On Fig. 9.1, sketch how the induced e.m.f. $E$ across the coil terminals varies with time $t$ at the higher rotational speed. Your graph should run from $t = 0$ to $t = 20\,\text{ms}$. Take $E = 0$ when $t = 0$.
State and explain the effect on the motion of the coil in (b) when a load resistor is connected across its terminals.