An inductor of inductance L , a capacitor of capacitance C and a...

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 $V$ ~volt& as shown in figure.Potential difference across& $L, C$ ~and& $R$ ~is $40V, 10V$ and $40V$ , respectively. The amplitude of current flowing through $\text{L-C-R}$ ~series circuit is $10\sqrt{2}A$ . The impedance of the circuit is :

An inductor of inductance L , a capacitor of capacitance C and a resistor of resistance R ~are connected in series to

Options

A $4\sqrt{2}Ω$
B $5 / \sqrt{2}Ω$
C $5Ω$
D $4Ω$

Correct answer

C. $5Ω$

Step-by-step solution

An inductor of inductance L , a capacitor of capacitance C and a resistor of resistance R ~are connected in series to

$V = \sqrt{{V}_{R}^{2} + {\left({V}_{C} - {V}_{L}\right)}^{2}}$

$= \sqrt{{40}^{2} + ( 10 - 40{)}^{2}}$

$= 50volt$

${i}_{rms} = \dfrac{{V}_{rms}}{Z}$

$⇒ Z = \dfrac{{v}_{rms}}{{i}_{rms}}$

$⇒ Z = \dfrac{{V}_{rms} \times \sqrt{2}}{10}$

$⇒ Z = \dfrac{\sqrt{2} \times 50}{10\sqrt{2}}$

$⇒ Z = 5Ω$

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