Question

(a) By means of a schematic circuit diagram illustrate the peak rectifier, if the supply voltage is v(t) = V Sin wt, what is the voltage across the load resistor? (6)

(b) A series circuit comprising a 50Ω resistor, a coil having resistance and inductance and a capacitor is connected across a 50 V variable frequency supply. When the frequency is 400 Hz the current reaches its maximum value of 0.6 A and the voltage across the capacitor is 200 V. Calculate EACH of the following: (10)

(i) the value of the capacitance;

(ii) the resistance and inductance of the coil;

(iii) the power taken from the supply;

(iv) the circuit power factor.

Answer 1

Part (a)

Operation and Output Voltage Across Load Resistor

Let the input supply be: v(t)=Vmsin(ωt)

During the positive half-cycle, the diode conducts whenever v(t) exceeds the voltage across the capacitor. The capacitor charges instantly (ideal case) to the peak value Vm.
After reaching the peak, the diode becomes reverse biased (since v(t)<Vm), and the capacitor holds its charge.
The load resistor (R) is connected in parallel with the capacitor; thus, the voltage across Ris the same as across C.
If we ignore the small discharge of C(assuming R is large and/or C is large so discharge is negligible between cycles):

Voltage Across Load Resistor

The voltage across R after initial peak is: vR(t)≈VmThat is, the output is a DC voltage nearly equal to the peak value of the AC input.

Mathematical Expression

If capacitor discharge is considered negligible: vout(t)=VmIf the discharge is not negligible (realistic case), the output will have slight ripple and can be given by: vout(t)≈Vm−ΔVwhere ΔV is the ripple voltage (depends on R, C, and frequency f).

✓ Verified Model Answer (Text Solution)

Operation and Output Voltage Across Load Resistor

Voltage Across Load Resistor

Mathematical Expression