The vector diagram of current and voltage for a circuit is as shown. The components of the circuit will be

$A$ direct current of $10 \,A$ is superimposed on an alternating current $I = 40 \cos \omega t \; (A)$ flowing through a wire. The effective value of the resulting current will be ....... $A$.

If $C, R, L$ and $I$ denote capacity,resistance,inductance and electric current respectively,the quantities having the same dimensions of time are :
$(1)$ $C R$
$(2)$ $\frac{L}{R}$
$(3)$ $\sqrt{L C}$
$(4)$ $L I^2$

An $AC$ generator consists of a coil of $100$ turns and is of cross-sectional area $3 \ m^2$. It is rotating at a constant angular speed of $60 \ rad \ s^{-1}$ in a uniform magnetic field of $0.04 \ T$. The resistance of the coil is $360 \ \Omega$. What is the maximum power dissipation in the coil (in $W$)?

In the shown $AC$ circuit,the phase difference between currents $I_1$ and $I_2$ is:

An $AC$ source of $20\,V$ (assuming standard frequency $f = 50\,Hz$ for calculation) is connected to an inductance of $100\,mH$,a capacitance of $100\,\mu F$,and a resistance of $120\,\Omega$ as shown in the figure. The time in which the resistance,having a thermal capacity of $2\,J/^{\circ}C$,will get heated by $16^{\circ}C$ is ..........$s$.