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: Understanding the Concept:
For a series LR circuit, the impedance is \(Z = \frac{V_{rms}}{I_{rms}}\), and the resistance is \(R = Z\cos\phi\), where \(\phi\) is the phase angle between voltage and current.

Step 2: Find the impedance:
\(Z = \frac{25}{0.5} = 50\ \Omega\).

Step 3: Find R:
\[ R = Z\cos\frac\pi3 = 50\times\frac12 = 25\ \Omega \]

Step 4: Why the other options are wrong.
50 \(\Omega\) is the full impedance (the value if \(\phi\) were zero). 20 \(\Omega\) and 40 \(\Omega\) do not match \(Z\cos60^{\circ}\).

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