In a LCR circuit having L = 8.0 henry, C = 0.5 $\mathrm{\mu F}$ and R = 100 $\mathrm{\Omega }$ in series, the resonance frequency (in Hz) is 

1.  $\frac{250}{\mathrm{\pi }}\mathrm{Hz}$

2.  $\frac{600}{\mathrm{\pi }}\mathrm{Hz}$

3.  $\frac{500}{\mathrm{\pi }}\mathrm{Hz}$

4.  $500 \mathrm{Hz}$

In an \(LCR\) series network, \(V_L = 40~\text{V}, V_C = 20~\text{V}~\text{and}~V_R = 15~\text{V}.\) The supply voltage will be:
1. \(25~\text{V}\)
2. \(75~\text{V}\)
3. \(35~\text{V}\)
4. zero

The ratio of the number of turns in secondary to primary in an ideal transformer varies from 50 to 550. If the power input is P, then its output power is  -

1.  11P

2.  $\frac{\mathrm{P}}{11}$

3.  $\frac{18P}{111}$

4.  P

Loss in energy in the transformer is due to 

1.  Hysteresis

2.  Eddy current loss

3.  Leakage of flux

4.  All of these

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