A source of $e.m.f.$ $E = 15\,V$ and having negligible internal resistance is connected to a variable resistance so that the current in the circuit increases with time as $i = 1.2 t + 3$. Then, the total charge that will flow in first five second will be ............... $C$
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A battery of internal resistance $4\,\Omega $ is connected to the network of the resistance as shown in Fig. If the maximum power can be delivered to the network, the magnitude of $R$ in $\Omega $ should be
Circuit for the measurement of resistance by potentiometer is shown. The galvanometer is first connected at point $A$ and zero deflection is observed at length $P J = 10\ cm$ . In second case it is connected at point $C$ and zero deflection is observed at a length $30\ cm$ from $P$ . Then the unknown resistance $X$ is
The circuit shown here is used to compare the emf of two cells $E_1$ and $E_2 (E_1 > E_2)$. The null point is at $C$ when the galvanometer is connected to $E_1$. When the galvanometer is connected to $E_2$, the null point will be
A potential $V_0$ is applied across a uniform wire of resistance $R$. The power dissipation is $P_1$. The wire is then cut into two equal halves and a potential of $V _0$ is applied across the length of each half. The total power dissipation across two wires is $P_2$. The ratio $P_2: P_1$ is $\sqrt{x}: 1$. The value of $x$ is $.............$.
A constant voltage is applied between the two ends of a metallic wire. If both the length and the radius of the wire are doubled, the rate of heat developed in the wire