Question

When an inductance '\(L\)' and resistor '\(R\)' are connected in series to \(25\)V, \(50\) Hz supply, a current of \(0.5\) A flows in the circuit. The current lags behind in phase from applied voltage by \((\frac{π}{3})\) radian. The value of R is \((cos60^{\circ} = \frac{1}{2})\)

• A. \(20\,\Omega\)
• B. \(25\,\Omega\)
• C. \(40\,\Omega\)
• D. \(50\,\Omega\)

Hint:

Z = V/I and R = Z cos(phi).

Answer 1

The Correct Option is B

Step 1: Use the power factor:
$\cos\phi = \frac RZ$.

Step 2: Insert values:
$\frac12 = \frac{R}{50}$, so $R = 25\ \Omega$.

Step 3: Check with the reactance:
$X_L = Z\sin60^{\circ} = 43.3\ \Omega$, and $\sqrt{25^2 + 43.3^2} = 50\ \Omega$, which equals $Z$.

Final Answer:
R equals 25 ohm, option (B). \[ \boxed{25\ \Omega} \]