An inductor of inductance , a capacitor of capacitance and a resistor of resistance are connected in series to an AC source of potential difference volts as shown in the figure. Potential difference across L, C and R is 40 V, 10 V and 40 V, respective

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Solution

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 the figure.

Potential difference across L, C and R is 40 V, 10 V and 40 V, respectively. The amplitude of current flowing through the LCR series circuit is $10 \sqrt{2}$ $A$ . The impedance of the circuit is [2021]

1 $5$ $Ω$

2 $4 \sqrt{2}$ $Ω$

3 $\frac{5}{\sqrt{2}}$ $Ω$

4 $4$ $Ω$

Ans.
(1)

Given, $V_{L} = 40$ $V$

$V_{C} = 10$ $V, V_{R} = 40$ $V$

$V_{rms} = \sqrt{V_{R}^{2} + {(V_{L} - V_{C})}^{2}} \Rightarrow V_{rms} = \sqrt{40^{2} + {(40 - 10)}^{2}} = 50$ $V$

$I_{0} = 10 \sqrt{2}$ $A \Rightarrow I_{rms} = \frac{I_{0}}{\sqrt{2}} = 10$ $A$

$Impedance, Z = \frac{V_{rms}}{I_{rms}} = \frac{50}{10} = 5$ $Ω$

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