Practice Generator in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A device that converts mechanical (kinetic) energy into electrical energy by rotating a coil of wire within a magnetic field, exploiting electromagnetic induction.

Spin a loop of wire between magnets and you get electricity — the changing flux induces a voltage that drives current through an external circuit.

Showing a random 20 of 50 problems.

Example 1

challenge
A generator delivers 5 kW5\text{ kW} at 250 V250\text{ V} RMS through a 1 Ω1\,\Omega transmission line. By what factor does line loss change if the same power is sent at 2500 V2500\text{ V} RMS?

Example 2

hard
A power-station generator produces 25 kV25\text{ kV} RMS at 50 Hz50\text{ Hz}. If the coil has N=500N=500 turns in B=1.2 TB=1.2\text{ T}, find the coil area.

Example 3

easy
A coil: N=10N=10, B=0.5B=0.5 T, A=0.2A=0.2 m2^2, ω=4\omega=4 rad/s. Find the peak EMF.

Example 4

hard
An AC generator's coil normal makes angle θ=ωt\theta = \omega t with B⃗\vec B. Show why the EMF magnitude is NBAω∣sin⁡(ωt)∣NBA\omega|\sin(\omega t)|, not cos⁡\cos.

Example 5

medium
A generator coil has 100100 turns and area 0.05 m20.05 \text{ m}^2 in a 0.4 T0.4 \text{ T} field. It needs to produce a peak EMF of 500 V500 \text{ V}. At what frequency must it rotate?

Example 6

medium
A generator's instantaneous EMF is E(t)=170sin⁡(120πt) V\mathcal{E}(t) = 170\sin(120\pi t)\text{ V}. What is the frequency?

Example 7

easy
A friend says a generator 'makes energy from spinning.' What is wrong with this statement?

Example 8

hard
A hydroelectric generator produces 10 MW10 \text{ MW} at 20,000 V20{,}000 \text{ V} RMS. What RMS current does it deliver? If the transmission line has 2 Ω2 \text{ } \Omega resistance, what percentage of power is lost in transmission?

Example 9

medium
A generator must produce a peak EMF of 200 V200\text{ V}. Given B=0.5 TB=0.5\text{ T}, A=0.04 m2A=0.04\text{ m}^2, ω=100 rad/s\omega = 100\text{ rad/s}, find the required number of turns.

Example 10

easy
What component must be added to a simple AC generator's coil terminals to make it output direct current?

Example 11

medium
True or false: a generator with a stationary coil and rotating magnet can also produce an EMF.

Example 12

medium
A generator coil has N=80N=80 turns, area A=0.02 m2A=0.02\text{ m}^2, in a field B=0.6 TB=0.6\text{ T}, and spins at f=60 Hzf=60\text{ Hz}. Find the peak EMF.

Example 13

hard
A wind-turbine generator rotates at ω=12 rad/s\omega = 12\text{ rad/s} with N=300N=300, B=0.8 TB=0.8\text{ T}, A=1.5 m2A=1.5\text{ m}^2. Find the average power dissipated in a 50 Ω50\,\Omega load.

Example 14

easy
A coil with N=25N=25, B=0.2 TB=0.2\text{ T}, A=0.1 m2A=0.1\text{ m}^2 rotates at ω=8 rad/s\omega=8\text{ rad/s}. Find the peak EMF.

Example 15

medium
A generator coil with peak EMF 80 V80\text{ V} drives a 20 Ω20\,\Omega resistor. Find the peak current and RMS power dissipated.

Example 16

easy
Name the physical principle a generator relies on to convert mechanical motion into an EMF.

Example 17

medium
A coil: N=50N=50, B=0.4B=0.4 T, A=0.1A=0.1 m2^2, ω=10\omega=10 rad/s. Find the peak EMF.

Example 18

medium
A 4-pole AC generator rotates mechanically at fmech=30 Hzf_{mech} = 30\text{ Hz}. What electrical frequency does it produce? (felec=(pole pairs)fmechf_{elec} = (\text{pole pairs}) f_{mech}.)

Example 19

hard
A generator coil drives a 40 Ω40\,\Omega load with Vrms=110 VV_{rms} = 110\text{ V}. The coil + connecting wires have internal resistance 5 Ω5\,\Omega. Find the load's average power.

Example 20

challenge
A generator delivers 120120 V RMS to a 10 Ω10\,\Omega load. Find the average power dissipated. (P=Vrms2/RP = V_{rms}^2/R.)
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