The power dissipated in a resistor of resistance $R$ when an alternating current with a peak value of $I_p$ flows through it is:

If the voltage and current in an ac circuit are respectively $50 \sin (50 t) \text{ V}$ and $50 \sin (50 t + \frac{\pi}{4}) \text{ mA}$,then the power dissipated in the circuit is nearly (in $W$)

$A$ series $LCR$ circuit is connected to an a.c. source of $230 \ V, 50 \ Hz$. The circuit contains a resistance of $80 \ \Omega$,an inductor having inductive reactance $70 \ \Omega$,and a capacitor of capacitive reactance $130 \ \Omega$. The power factor of the circuit is $x$. The value of $x$ is

$A$ $LCR$ series circuit driven with $V_{rms} = 90 \text{ V}$ at frequency $f_d = 30 \text{ Hz}$ has resistance $R = 80 \text{ }\Omega$, an inductance with inductive reactance $X_L = 20.0 \text{ }\Omega$ and capacitance with capacitive reactance $X_C = 80.0 \text{ }\Omega$. The power factor of the circuit is . . . . . . .

What is power factor and voltage-current relationship in an $AC$ circuit?

$A$ circuit,consisting of an inductance and a resistance in series,is connected to a $250 \ V$ $A$.$C$. supply. It draws a current of $10 \ A$. If the power consumed in the circuit is $1500 \ W$,calculate the wattless current. (in $A$)