Question

Given below are the two circuits, choose the correct option.

• A. At resonance, current in (B) is less than that in (A)
• B. The r.m.s. current in (B) can be larger than that in (A)
• C. The r.m.s. current in (A) is always equal to that in (B)
• D. The r.m.s. current in (B) can never be larger than that in (A)

Hint:

The impedance of circuit B is at least R, so its current cannot exceed V over R, the current of circuit A.

Answer 1

The Correct Option is D

Step 1: Approach
Compare through the power or the impedance triangle.

Step 2: Idea
The resistor is the same in both. In B the reactances add a perpendicular component to the impedance, which can only make the magnitude larger: $Z_B\ge R=Z_A$.

Step 3: Consequence
With the same voltage, $I_B=V/Z_B\le V/Z_A=I_A$. The two are equal only when $X_L=X_C$ (resonance), which does not hold at 50 Hz here since $X_C$ is about 7960 ohm and $X_L$ is about 12.6 ohm.

Step 4: Answer
Option (D).

Final Answer:
The impedance of B is never smaller than 30 ohm, so its current never exceeds the 7 A in A, option (D). \[ \boxed{\text{(D)}} \]