Question

In an alternating current circuit consisting of elements in series, the current increases on increasing the frequency of supply. Which of the following elements are likely to constitute the circuit?

1. Only resistor.
2. Resistor and an inductor.
3. Resistor and a capacitor.
4. Only a capacitor.

Options

• b and c

• a and d

• b and d

• c and d

Answer 1

c and d

Explanation:

This is a similar problem as we discussed above. In this problem, the current increases on increasing the frequency of supply. Hence, the reactance of the circuit must be decreased as increase in frequency. So, one element that must be connected is the capacitor. We can also connect a resistor in series.

For a capacitive circuit,

X_C = 1/ωC = 1/2πfC

When frequency increases, X_C decreases. Hence current in the circuit increases.

Important point: Resistive, Capacitive CIrcuit (RC - Circuit)

V_R = i_R,

V_C = iX_C,

V_R = iR

1. Applied voltage: `V = sqrt(V_R^2 + V_C^2)`
2. Impedance: `Z = sqrt(R^2 + X_C^2) = sqrt(R^2 + (1/(ωC)^2)`
3. Current: `i = i_0 sin(ωt + phi)`
4. Peak current: `I_0 = V_0/Z = V_0/sqrt(R^2 + X_C^2) = V_0/sqrt(R^2 + 1/(4pi^2v^2C^2)`
5. Phase difference: `phi = tan^-1  X_C/R = tan^-1  1/(ωCR)`
6. Power factor: `cos phi = R/sqrt(R^2 + X_C^2)`
7. Leading quantity: Current