(B) Given,peak voltage $V_0 = 150 \text{ V}$ and peak current $I_0 = 5 \text{ A}$.Phase difference $\phi = (100 \pi t + \pi) - (100 \pi t + \frac{2 \p

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(B) Given,peak voltage $V_0 = 150 \text{ V}$ and peak current $I_0 = 5 \text{ A}$.Phase difference $\phi = (100 \pi t + \pi) - (100 \pi t + \frac{2 \pi}{3}) = \frac{\pi}{3} = 60^{\circ}$.Average power dissipated $P_{av} = V_{rms} I_{rms} \cos \phi = \frac{V_0}{\sqrt{2}} \cdot \frac{I_0}{\sqrt{2}} \cos 60^{\circ} = \frac{150 \times 5}{2} \times \frac{1}{2} = 187.5 \text{ W}$.Impedance $Z = \frac{V_0}{I_0} = \frac{150}{5} = 30 \Omega$.Since $\cos \phi = \frac{R}{Z}$,we have $R = Z \cos 60^{\circ} = 30 \times 0.5 = 15 \Omega$.

Class 12 Physics Alternating Current RL, RC and LC AC Circuits

Medium

$A$ resistor and an inductor are connected in series to an $AC$ source of voltage $V = 150 \sin (100 \pi t + \pi) \text{ V}$. If the current in the circuit is $I = 5 \sin (100 \pi t + \frac{2 \pi}{3}) \text{ A}$,then the average power dissipated and the resistance of the resistor are respectively:

AP EAMCET 2018 All AP EAMCET

A
$187.5 \text{ W}, 30 \Omega$
B
$187.5 \text{ W}, 15 \Omega$
C
$375 \text{ W}, 30 \Omega$
D
$375 \text{ W}, 15 \Omega$

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Alternating Current

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RL, RC and LC AC Circuits

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$A$ resistor and an inductor are connected in series to an $AC$ source of voltage $V = 150 \sin (100 \pi t + \pi) \text{ V}$. If the current in the circuit is $I = 5 \sin (100 \pi t + \frac{2 \pi}{3}) \text{ A}$,then the average power dissipated and the resistance of the resistor are respectively:

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$A$ resistance of $200 \ \Omega$ and an inductor of $\frac{1}{2 \pi} \ H$ are connected in series to an a.c. voltage of $40 \ V$ and $100 \ Hz$ frequency. The phase angle between the voltage and current is

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$A$ coil of inductance $0.50 \; H$ and resistance $100 \; \Omega$ is connected to a $240 \; V, 50 \; Hz$ $AC$ supply.$(a)$ What is the maximum current in the coil?$(b)$ What is the time lag between the voltage maximum and the current maximum?

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$A$ coil of inductance $0.50 \; H$ and resistance $100 \; \Omega$ is connected to a $240 \; V, 50 \; Hz$ $AC$ supply.
$(a)$ What is the maximum current in the coil?
$(b)$ What is the time lag between the voltage maximum and the current maximum?