The potential difference V and the current i flowing through an instrument in an ac circuit of frequency f are given by $V=5\cos \omega t$ volts and I = 2 sin ωt amperes (where ω = 2πf). The power dissipated in the instrument is 

(1) Zero

(2) 10 W

(3) 5 W

(4) 2.5 W

If a current I given by $I_0\sin \left(\omega t-\frac{{\displaystyle \pi }}{{\displaystyle 2}}\right)$ flows in an ac circuit across which an ac potential of $E=E_0\sin \omega t$ has been applied, then the power consumption P in the circuit will be 

(1) $P=\frac{E_0{I}_0}{\sqrt{2}}$

(2) $P=\sqrt{2}{E}_0{I}_0$

(3) $P=\frac{E_0{I}_0}{2}$

(4) P = 0

In an AC circuit, the current is given by; $i=5\sin\left(100t-\frac{\pi}{2}\right)$ and the AC potential is $V =200\sin(100 t)~\text V.$ The power consumption is:
1. $20~\text W$
2. $40~\text W$
3. $1000~\text W$
4. zero

In an $LCR$ circuit having $L = 8.0~\text{H}$, $C= 0.5~\mu\text{F}$ and $R = 100~\Omega$ in series, what is the resonance frequency?
1. $600$ radian/sec
2. $600$ Hz
3. $500$ radian/sec
4. $500$ Hz

A circuit consists of $3$ ohms of resistance and $4$ ohms of reactance. The power factor of the circuit is: