In the given circuit, the AC source has $ω = 100 rad / s .$ Considering the inductor and capacitor to be ideal, the correct choice(s) is (are) [2012]

Question

Smart Achievers · Accepted Answer

(1, 3)

$Impedance across A B, RC part of the circuit.$

$Z_{1} = \sqrt{X_{C}^{2} + R_{1}^{2}} = \sqrt{{(\frac{1}{ω C})}^{2} + R_{1}^{2}}$

$= \sqrt{{(100)}^{2} + {(100)}^{2}} = 100 \sqrt{2}$

$∴$ $I_{1} = \frac{V}{Z_{1}} = \frac{20}{100 \sqrt{2}}$ $(Current leads emf by ϕ_{1})$

where $\cos ϕ_{1} = \frac{R}{Z_{1}} = \frac{100}{100 \sqrt{2}} = \frac{1}{\sqrt{2}} \Rightarrow ϕ = 45 °$

$Impedance across C D, LR part of the circuit.$

$Z_{2} = \sqrt{X_{L}^{2} + R_{2}^{2}} = \sqrt{{(ω L)}^{2} + R_{2}^{2}}$

$= \sqrt{{(0.5 \times 100)}^{2} + {(50)}^{2}} = 50 \sqrt{2} Ω$

$∴$ $I_{2} = \frac{V}{Z_{2}} = \frac{20}{50 \sqrt{2}}$ $(Current lags emf by ϕ_{2})$

where $\cos ϕ_{2} = \frac{R}{Z_{2}} = \frac{50}{50 \sqrt{2}} = \frac{1}{\sqrt{2}}$ $\Rightarrow ϕ_{2} = 45 °$

$∴$ $Current I from the circuit$

$I = \frac{20}{100 \sqrt{2}} + \frac{20}{50 \sqrt{2}} = I_{1} + I_{2} = 0.3 A$

Solution

Q.
In the given circuit, the AC source has $ω = 100 rad / s .$ Considering the inductor and capacitor to be ideal, the correct choice(s) is (are) [2012]

1 The current through the circuit, $I$ is 0.3 A

2 The current through the circuit, $I$ is $0.3 \sqrt{2} A$

3 The voltage across $100 Ω$ resistor is $10 \sqrt{2} V$

4 The voltage across $50 Ω$ resistor is $10 V$

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Solution

Q. In the given circuit, the AC source has ω=100 rad/s. Considering the inductor and capacitor to be ideal, the correct choice(s) is (are) [2012]

1 The current through the circuit, I is 0.3 A

2 The current through the circuit, I is 0.32A

3 The voltage across 100 Ω resistor is 102V