(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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AP EAMCET 2018 Paper All AP EAMCET years →

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Medium

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DifficultJEE MAIN 2024

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DifficultMHT CET 2021

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Easy

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MediumAIIMS 2018

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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:

Similar Questions

$A$ radio can tune over the frequency range of a portion of $MW$ broadcast band: ($800 \;kHz$ to $1200 \;kHz$). If its $LC$ circuit has an effective inductance of $200 \;\mu H$,what must be the range of its variable capacitor?

$A$ bulb and a capacitor are connected in series across an $AC$ supply. $A$ dielectric is then placed between the plates of the capacitor. The glow of the bulb:

For a series $LCR$ circuit,which one of the following is a $CORRECT$ statement?

$A$ sinusoidal voltage of peak value $283\,V$ and frequency $50\,Hz$ is applied to a series $LCR$ circuit in which $R = 3\,\Omega$,$L = 25.48\,mH$,and $C = 796\,\mu F$. Find the impedance of the circuit in $\Omega$.

In a series $R-C$ circuit shown in the figure,the applied voltage is $10\, V$ and the voltage across the capacitor is found to be $8\, V$. Then,the voltage across $R$ and the phase difference between the current and the applied voltage will respectively be

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