Q 12-07-009NEETNEET 2021Top questionMedium
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 :
Answer: (A) $5\ \Omega$
The given voltages are rms values. Source voltage:
$$V = \sqrt{V_R^2 + (V_L - V_C)^2} = \sqrt{40^2 + (40 - 10)^2} = 50\ \text{V}$$
rms current: $I_{rms} = \dfrac{10\sqrt{2}}{\sqrt{2}} = 10$ A.
$$Z = \frac{V}{I_{rms}} = \frac{50}{10} = 5\ \Omega$$
Solution by Sreeraj P, M.Sc Physics