Part (a) Solution

(i) Resonant Frequency and Impedance Graph [1.5 Marks]

Step 1 (Formula): [0.5 Mark]
The resonant frequency $f_r$ of a series LCR circuit is given by the condition where inductive reactance equals capacitive reactance ($X_L = X_C$):

Thus, $f_r = \frac{1}{2\pi\sqrt{LC}}$. The factors are Inductance ($L$) and Capacitance ($C$).

Step 2 (Graph): [1.0 Mark]
The impedance $Z = \sqrt{R^2 + (\omega L - \frac{1}{\omega C})^2}$. At resonance, $Z = R$ (minimum). The graph is a U-shaped curve plotted between $Z$ and frequency $f$.

(ii) Step-up Transformer [2.0 Marks]

Step 1 (Diagram/Working): [1.0 Mark]
A step-up transformer consists of two coils (primary and secondary) wound on a soft iron core. In a step-up transformer, the number of turns in the secondary coil ($N_s$) is greater than the number of turns in the primary coil ($N_p$).

Step 2 (Principle): [1.0 Mark]
Based on Faraday's Law of Induction, the changing magnetic flux in the primary coil induces an EMF in the secondary coil. Since $N_s > N_p$, the output voltage $V_s > V_p$.

(iii) Energy Losses [1.5 Marks]

• Copper Loss: Heat produced due to the resistance of the windings ($I^2R$ loss).
• Eddy Current Loss: Induced currents in the iron core causing heating.

Part (b) Solution

(i) AC Generator [2.5 Marks]

Construction: Consists of a rectangular coil rotating in a uniform magnetic field between two pole pieces of a magnet. The ends are connected to slip rings and carbon brushes.

Working: As the coil rotates, the magnetic flux $\phi = BA \cos(\theta) = BA \cos(\omega t)$ linked with it changes. By Faraday's Law, induced EMF $\varepsilon = - \frac{d\phi}{dt} = BA\omega \sin(\omega t)$.

(ii) Magnetic Moment of Electron [2.5 Marks]

Step 1 (Formula): [1.0 Mark]
Magnetic moment $\mu = I \cdot A$. The current $I$ created by an electron moving with speed $v$ in a circle of radius $r$ is $I = \frac{e}{T}$, where $T = \frac{2\pi r}{v}$.

Step 2 (Substitution): [1.0 Mark]
$$ I = \frac{e}{2\pi r / v} = \frac{ev