In a series $L C R$ circuit, the inductance, capacitance and resistance are $L = 100 m H, C = 100 μ F$ and $R = 10 Ω$ respectively. They are connected to an $A C$ source of voltage $220 V$ and frequency of $50 H z$ . The approximate value of current in the circuit will be $A$ .

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Solution

Inductive reactance, $X_{L} = L ω = 100 \times 10^{- 3} \times 2 π \times 50 = 10 π Ω$

Capacitive reactance, $X_{C} = \frac{1}{ω C} = \frac{1}{2 π \times 50 \times 100 \times 10^{- 6}} = \frac{100}{π} Ω$

Impedence,

$Z = \sqrt{R^{2} + (X_{L} - X_{C})^{2}}$

$= \sqrt{10^{2} + {[10 π - \frac{100}{π}]}^{2}}$

$\approx 10 Ω$

$\Rightarrow$ Current $= \frac{V}{Z} = \frac{220}{10} A = 22 A$

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In a series LCR circuit, the inductance, capacitance and resistance are L=100 mH,C=100 μF and R=10 Ω respectively. They are connected to an AC source of voltage 220 V and frequency of 50 Hz. The approximate value of current in the circuit will be A.

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In a series $L C R$ circuit, the inductance, capacitance and resistance are $L = 100 m H, C = 100 μ F$ and $R = 10 Ω$ respectively. They are connected to an $A C$ source of voltage $220 V$ and frequency of $50 H z$ . The approximate value of current in the circuit will be $A$ .