Question

For the given figures, choose the correct options:

• A. At resonance, current in (b) is less than that in (a)
• B. The rms current in circuit (b) can never be larger than that in (a)
• C. The rms current in figure(a) is always equal to that in figure (b)
• D. The rms current in circuit (b) can be larger than that in (a)

Answer 1

The Correct Option is B

Step 1: Impedance in Circuit (a):
Circuit (a) consists only of a resistor. The total impedance is: \[ Z_a = R \] This results in the maximum possible rms current for a given voltage: \[ I_a = \frac{V}{R} \] Step 2: Impedance in Circuit (b):
Circuit (b) consists of a resistor and reactive components (inductor and capacitor). The total impedance is: \[ Z_b = \sqrt{R^2 + (X_L - X_C)^2} \] Since \(|X_L - X_C| \geq 0\), the impedance in circuit (b) is always greater than or equal to \(R\): \[ Z_b \geq Z_a \] Step 3: Compare the rms currents:
The rms current in circuit (b) is: \[ I_b = \frac{V}{Z_b} \] Since \(Z_b \geq Z_a\), it follows that: \[ I_b \leq I_a \] Hence, the rms current in circuit (b) can never exceed that in circuit (a).