COMEDK · Physics · 23. Alternating Current
In the A. C. circuit given below, an inductor, capacitor, and resistor (\(R = 110\text{ }\Omega\)) are in series with a \(220\text{ V}, 50\text{ Hz}\) source. Voltmeters \(V_1\) (across the inductor) and \(V_2\) (across the capacitor) read \(100\text{ V}\) each. Find the reading of the voltmeter \(V_3\) (across the resistor) and the ammeter A.
- A 110 V, 2 A
- B 220 V, 1 A
- C 220 V, 2 A
- D 110 V, 4 A
Answer & Solution
Correct Answer
(C) 220 V, 2 A
Step-by-step Solution
Detailed explanation
\(V_L = V_C = 100\) V, so they cancel (circuit is at resonance). \(V = \sqrt{V_R^2 + (V_L - V_C)^2} = \sqrt{V_R^2 + 0}\) \(220 = V_R \Rightarrow V_3 = 220\) V At resonance, \(Z = R = 110\ \Omega\) \(I = \dfrac{V_R}{R} = \dfrac{220}{110} = 2\) A
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