**Mean and r m s values in AC circuits; DC and AC circuits with R, L and C components; Series and parallel resonances; Quality factor; Principle of transformer.**

Questions:

**Q 1. **A $10 \Omega$ resistor is connected in series with a capacitor of $1 \mu F$ and a battery with emf $12V$. Before the switch is closed at time $t=0$, the capacitor is uncharged. Calculate the following: (i) The time constant (ii) What fraction of the final charge is on the plates at the time $t=46 s.$(iii) What fraction of the initial current remains at the time $t=46s.$ Consider that the internal resistance of the battery is zero and neglect the resistance of all the connecting wires. ** [15 marks]**

**Q 2. ** A series RLC circuit has $R= 2 \Omega$ . The energy stored in the circuit decreases by 1% per period of oscillation. Its natural undamped frequency is $2 kHz$ . Determine the values of the inductor and the quality factor.**[15 marks]**

Video Solution at 11 pm