Question:
The alternating voltage and current in an electric circuit are respectively given by \(E = 100\sin 100\pi t\), \(I = 5\sin 100\pi t\). The reactance of the circuit will be
The alternating voltage and current in an electric circuit are respectively given by \(E = 100\sin 100\pi t\), \(I = 5\sin 100\pi t\). The reactance of the circuit will be
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When E and I are in phase, the circuit is purely resistive. The ratio \(E_0/I_0\) gives impedance \(Z\), and \(X = Z\sin\phi = 0\) here.
Updated On: Apr 20, 2026
- \(1\,\Omega\)
- \(0.05\,\Omega\)
- \(20\,\Omega\)
- zero
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
When voltage and current are in phase (\(\phi = 0\)): circuit is purely resistive, no reactance present. Impedance: \(Z = \frac{E_{\rm rms}}{I_{\rm rms}}\).
Step 2: Detailed Explanation:
Given peak values: \(Z = \frac{E_0}{I_0} = \frac{100}{5} = 20\,\Omega\). Since \(\phi = 0\): \(R = Z = 20\,\Omega\). Reactance: \(X = Z\sin\phi = 0\). Thus, the circuit is purely resistive and impedance equals resistance.
Step 3: Final Answer:
\[ \boxed{Z = 20\,\Omega,\quad R = 20\,\Omega,\quad X = 0\,\Omega} \]
When voltage and current are in phase (\(\phi = 0\)): circuit is purely resistive, no reactance present. Impedance: \(Z = \frac{E_{\rm rms}}{I_{\rm rms}}\).
Step 2: Detailed Explanation:
Given peak values: \(Z = \frac{E_0}{I_0} = \frac{100}{5} = 20\,\Omega\). Since \(\phi = 0\): \(R = Z = 20\,\Omega\). Reactance: \(X = Z\sin\phi = 0\). Thus, the circuit is purely resistive and impedance equals resistance.
Step 3: Final Answer:
\[ \boxed{Z = 20\,\Omega,\quad R = 20\,\Omega,\quad X = 0\,\Omega} \]
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