Super position theorem

Q.

An alternating current is given by the equation $i=i_1\sin \omega t+i_2\cos \omega t$. The rms current will be:

1. $\frac{1}{2}{({i_1}^2+{i_2}^2)}^{1/2}$

2. $\frac{1}{\sqrt{2}}{({i_1}^2+{i_2}^2)}^{1/2}$

3. $\frac{1}{\sqrt{2}}{(i_1+i_2)}^2$

4. $\frac{1}{\sqrt{2}}(i_1+i_2)$

Q. The rms value of the current in a wire which carries a d.c current of 10A and a sinusoidal alternating current of peak value 20 A is

1. 10 A
2. 14.14 A
3. 15 A
4. 17.32 A

Q. The power dissipated by the 10 $\Omega$ resistor in the circuit shown below is ______ W.

1. 3.32

Q. A periodic waveform $f\left(t\right)=(2-3\cos 10t{)}^{2}V$ is given.
Its rms value will be

1. $3.61V$
2. $10.80V$
3. $12.42V$
4. $77.18V$

Q.
Find the values of currents $I_1$ & $I_2$

1. $7sin3t$, zero
2. $5sin2t,5+5sin2t$
3. $5,5sin2t$
4. $5+5sin2t$, zero

Q.
Find the root mean square value of voltage $V_X$ in the figure shown.

1. $15.53V$
2. $7.83V$
3. $11.83V$
4. $2.88V$