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An inductor-coil, a capacitor and an AC source of rms voltage 24V are connected in series. When the frequency of the source is varied, a maximum rms current of 6.0 A is observed. If this inductor coil and capacitor is connected to a battery of emf 12V and internal resistance 4.0 $Ω$ , what will be the current?

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2.5 A

0.5 A

2 A

1.5 A

answer is B.

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Detailed Solution

$V_{rms} = 24 V, I_{rms} = 6 A; V_{rms}^{1} = 12 V, r = 4 Ω$

$\begin{array}{l} I_{rms} = \frac{V_{rms}}{Z} \Rightarrow 6 = \frac{24}{Z} \Rightarrow Z = 4 Ω \\ I_{dc} = \frac{V}{r + Z} = \frac{12}{4 + 4} = 1 .5 A \end{array}$

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