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Q.

An inductor of inductance L, a capacitor of capacitance C and a resistor of resistance 'R' are connected in series to an ac source of potential difference V volts as shown in figure. Potential difference across L, C and R is 40 V, 10 V and 40 V, respectively. The amplitude of current flowing through LCR series circuit is 10 $\sqrt{2}$ A. The impedance of the circuit is :

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a

5 $Ω$

b

$4 \sqrt{2} Ω$

c

$5 / \sqrt{2} Ω$

d

4 $Ω$

answer is A.

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Detailed Solution

Supply voltage, $V = \sqrt{{(V_{L} - V_{C})}^{2} + V_{R}^{2}}$
$\Rightarrow V = \sqrt{(40 - 10)^{2} + 40^{2}} volt = 50 volt$
So peak value of supply voltage = $50 \sqrt{2} volt$
$\begin{array}{l} ∴ Z = 50 \sqrt{2} / 10 \sqrt{2} \\ = 5 Ω ∴ Z = 5 Ω \end{array}$

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