In an LR-circuit,the inductive reactance is e | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The average power consumed in an $AC$ circuit is given by $P = E_{rms} I_{rms} \cos \phi$,where $\cos \phi$ is the power factor.We know that $E_{r

Vedclass · Accepted Answer

$\frac{E_0^2}{4R}$

Vedclass · Answer

(C) The average power consumed in an $AC$ circuit is given by $P = E_{rms} I_{rms} \cos \phi$,where $\cos \phi$ is the power factor.We know that $E_{rms} = \frac{E_0}{\sqrt{2}}$ and $I_{rms} = \frac{I_0}{\sqrt{2}} = \frac{E_0}{Z\sqrt{2}}$.The power factor is $\cos \phi = \frac{R}{Z}$.Substituting these values,we get $P = \left(\frac{E_0}{\sqrt{2}}\right) \left(\frac{E_0}{Z\sqrt{2}}\right) \left(\frac{R}{Z}\right) = \frac{E_0^2 R}{2Z^2}$.Given that the inductive reactance $X_L = R$,the impedance $Z$ is calculated as $Z = \sqrt{R^2 + X_L^2} = \sqrt{R^2 + R^2} = \sqrt{2}R$.Substituting $Z^2 = 2R^2$ into the power formula: $P = \frac{E_0^2 R}{2(2R^2)} = \frac{E_0^2 R}{4R^2} = \frac{E_0^2}{4R}$.

In an $LR$-circuit,the inductive reactance is equal to the resistance $R$ of the circuit. An e.m.f. $E = E_0 \cos(\omega t)$ is applied to the circuit. The power consumed in the circuit is:

Similar Questions

For the given $RL$ circuit,the maximum power loss across the circuit can be $W$.

$A$ circuit is made of $1 \Omega$ resistance and $2.5 \text{ mH}$ inductance in series. If an alternating source of $200 \text{ V}$ and $50 \text{ Hz}$ is connected to the circuit,then the phase difference between current and voltage is . . . . . . .

$A$ $100 \;\mu\,F$ capacitor in series with a $40\; \Omega$ resistance is connected to a $110\; V, 60\; Hz$ supply.
$(a)$ What is the maximum current in the circuit?
$(b)$ What is the time lag between the current maximum and the voltage maximum?

$A$ coil having an inductance of $\frac{1}{\pi} \text{ H}$ is connected in series with a resistance of $300 \text{ } \Omega$. If an $A$.$C$. source $(20 \text{ V}, 200 \text{ Hz})$ is connected across the combination,the phase angle between voltage and current is

Vedclass Test Series

Exam Paper Generator

Online Exam Module