$A$ direct current of $4\,A$ and an alternating current of peak value $4\,A$ flow through resistances of $3\,\Omega$ and $2\,\Omega$ respectively. The ratio of heat produced in the two resistances in the same interval of time will be.

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

You are given many resistances,capacitors and inductors. These are connected to a variable $DC$ voltage source (the first two circuits) or an $AC$ voltage source of $50 \ Hz$ frequency (the next three circuits) in different ways as shown in Column $II$. When a current $I$ (steady state for $DC$ or rms for $AC$) flows through the circuit,the corresponding voltage $V_1$ and $V_2$ (indicated in circuits) are related as shown in Column $I$. Match the two.

If $L, C$ and $R$ represent inductance,capacitance and resistance respectively,then which of the following does not represent the dimensions of frequency?

If $L$,$C$,and $R$ are the self-inductance,capacitance,and resistance respectively,which of the following does not have the dimension of time?

There is a $100\,\Omega$ resistance in an $L-C-R$ $AC$ circuit. An $AC$ $emf$ of $200\,V$ and $\omega = 300\,rad/s$ is applied to this circuit. When only the capacitor is removed,the current lags the voltage by $60^o$. When only the inductor is removed,the current leads the voltage by $60^o$. The current in this $L-C-R$ circuit will be.....$A$