Exercises: Motors, Generators, and Transformers

An electric motor converts electrical energy to mechanical energy. What is the fundamental physical principle that causes the coil in a motor to rotate?

How does a generator differ from a motor in terms of energy conversion and operating principle?

A transformer has $N_p$ turns in the primary coil and $N_s$ turns in the secondary coil, with voltages $V_p$ and $V_s$. Which equation correctly states the turns ratio?

In a DC motor, a commutator reverses the current direction every half turn. Why is this necessary?

A generator coil rotates in a uniform magnetic field. How does the induced EMF vary with time as the coil rotates?

A step-up transformer has $N_p = 50$ turns in the primary coil and $N_s = 500$ turns in the secondary coil. The primary voltage is $V_p = 120\ \text{V}$. Calculate the secondary voltage $V_s$ in volts.

A transformer has a primary voltage of $V_p = 240\ \text{V}$ and a secondary voltage of $V_s = 12\ \text{V}$. If the primary coil has $N_p = 1000$ turns, how many turns does the secondary coil have?

An ideal transformer has primary voltage $V_p = 120\ \text{V}$ and secondary voltage $V_s = 1200\ \text{V}$. The primary current is $I_p = 10\ \text{A}$. Using power conservation ($V_p I_p = V_s I_s$), calculate the secondary current $I_s$ in amperes.

An electric vehicle uses the same electric machine as both a motor (when driving) and a generator (when braking). During regenerative braking, what happens?

A wind turbine generates electricity. Trace the energy conversions from wind to electricity in the correct order.

A transformer has $N_s / N_p = 5$. Because $N_s > N_p$, this is a   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   transformer. The secondary voltage is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   times the primary voltage, and the secondary current is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   times the primary current.

A step-up transformer with a turns ratio of $N_s/N_p = 10$ receives $P = 500\ \text{W}$ of electrical power at its primary. Assuming the transformer is ideal, how much power is delivered at the secondary?

In the electrical grid, step-up transformers raise voltage for long-distance transmission. Why must these transformers use AC rather than DC?

A power adapter for a laptop converts household voltage to a lower voltage. The primary coil connects to $V_p = 120\ \text{V}$ AC. The secondary coil has $N_s = 250$ turns and produces $V_s = 19.5\ \text{V}$ for the laptop.

How many turns does the primary coil have? Round to the nearest whole number.

A hydroelectric generator has a coil with $N = 500$ turns, each of area $A = 0.20\ \text{m}^2$, rotating in a magnetic field $B = 0.80\ \text{T}$ at angular velocity $\omega = 2\pi \times 60\ \text{rad/s}$ (60 Hz). The peak EMF is given by $\varepsilon_\text{max} = NBA\omega$.

Calculate the peak EMF of the generator in volts. Use $\pi \approx 3.14$.

What is wrong with this claim?

What is the fundamental error in this explanation?

A power plant generates $P = 5\ \text{MW}$ at $20{,}000\ \text{V}$. Two scenarios:

Scenario A: Power is transmitted at $20{,}000\ \text{V}$ (no step-up transformer).
Scenario B: A step-up transformer raises the voltage to $400{,}000\ \text{V}$.

The transmission line has resistance $R_\text{line} = 10\ \Omega$ in both scenarios.

Calculate the ratio of power lost in Scenario A to power lost in Scenario B. (That is, compute $P_\text{loss,A} / P_\text{loss,B}$.)

Explain why the "War of Currents" in the 1880s (AC vs. DC) was ultimately decided in favor of AC. Your answer should explain why DC could not be efficiently transmitted over long distances and what role the transformer played in AC's victory.