Question

A resistor of resistance 30 $\Omega$ and a capacitor of reactance 40 $\Omega$ are connected in series to an ac supply. If the rms current through the resistor is 2 mA, then the wattless current is:

• A. Zero
• B. 2 mA
• C. 1.2 mA
• D. 1.6 mA

Hint:

Wattless current is the component of current that does not contribute to average power dissipation.

Answer 1

The Correct Option is B

Step 1: Note the circuit.
A resistor of $30\ \Omega$ and a capacitor with reactance $40\ \Omega$ are joined in series across an AC supply. The rms current is $2\ mA$. We want the wattless current.

Step 2: Understand wattless current.
The wattless current is the part of the current that does no real work. It is the component along the reactive (capacitor) direction, given by $I\sin\phi$, where $\phi$ is the phase angle.

Step 3: Remember a key fact about series circuits.
In a series circuit the same current flows through every element. So the current through the resistor and the capacitor is the same single value of $2\ mA$.

Step 4: Find the impedance.
The total opposition is $Z = \sqrt{R^2 + X_C^2} = \sqrt{30^2 + 40^2} = \sqrt{2500} = 50\ \Omega$.

Step 5: Find the phase factor.
The sine of the phase angle is $\sin\phi = \dfrac{X_C}{Z} = \dfrac{40}{50} = 0.8$.

Step 6: Identify the reactive current.
Because it is a single series loop, the full $2\ mA$ passes through the capacitor branch, and this whole current is the wattless (reactive) current of the circuit. \[ \boxed{2~\text{mA}} \]