TS EAMCET · Physics · Alternating Current
The inductance L, Capacitance C and resistance R are the values of the components connected in series to an ac source of angular frequency \(\omega\). The inductive and capacitive reactances are \(X_L\) and \(X_C\) respectively. If the circuit is purely resistive, then
- A \(\mathrm{L}=\mathrm{C}\)
- B \(X_L=X_C\)
- C \(\omega \mathrm{L}=\omega \mathrm{C}\)
- D \(\mathrm{R}=\mathrm{L}=\mathrm{C}\)
Answer & Solution
Correct Answer
(B) \(X_L=X_C\)
Step-by-step Solution
Detailed explanation
The impedance of an RLC series circuit is \(Z=\sqrt{R^2+(X_L-X_C)^2}\). For a purely resistive circuit, \(Z=R\). \(R=\sqrt{R^2+(X_L-X_C)^2}\) \(R^2=R^2+(X_L-X_C)^2\) \(0=(X_L-X_C)^2\) \(X_L=X_C\)
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