or $\mathrm{E}_{1}-\left(\mathrm{i}_{1}+\mathrm{i}_{2}\right) \mathrm{R}-\mathrm{i}_{1} \mathrm{r}_{1}=0$
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Two coils require $20$ minutes and $60$ minutes respectively to produce same amount of heat energy when connected separately to the same source. If they are connected in parallel arrangement to the same source; the time required to produce same amount of heat by the combination of coils, will be________ $min$
In a potentiometer circuit a cell of $EMF$ $1.5\, {V}$ gives balance point at $36\, {cm}$ length of wire. If another cell of $EMF$ $2.5\, {V}$ replaces the first cell, then at what length of the wire, the balance point occurs ? (in $cm$)
In the balanced condition, the values of the resistances of the four arms of a Wheatstone bridge are shown in the figure below. The resistance $R_3$ has temperature coefficient $0.0004{ }^{\circ} C ^{-1}$. If the temperature of $R_3$ is increased by $100{ }^{\circ} C$, the voltage developed between $S$ and $T$ will be. . . . . . . volt.
A cell of $e.m.f.$ $1.5\,V$ having a finite internal resistance is connected to a load resistance of $2\,\Omega $. For maximum power transfer the internal resistance of the cell should be ............. $ohm$
A resistance of $2\,\Omega $ is connected across one gap of a meter-bridge and unknown resistance, greater than $2\,\Omega $ , is connected a cross the other gap. When these resistances are interchanged, the balance point shifts by $20\ cm$ , neglecting any end correction, the unknown resistance is ................ $\Omega$
In the circuit shown in the figure $K_1$ is open. The charge on capacitor $C$ in steady state is $q_1$. Now key is closed and at steady state charge on $C$ is $q_2$. The ratio of charges $q_1/q_2$ is