A battery of $e.m.f.$ $10\, V$ and internal resistance $3\,\Omega $ is connected to a resistor as shown in the figure. If the current in the circuit is $0.5\, A$. then the resistance of the resistor will be ............. $\Omega$
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$A$ battery of $\mathrm{emf}$ $E_0 = 12\, V$ is connected across a $4\,m$ long uniform wire having resistance $4\,\Omega /m$. The cells of small $\mathrm{emfs}$ $\varepsilon_1 = 2\,V$ and $\varepsilon_2 = 4\,V$ having internal resistance $2\Omega$ and $6\Omega$ respectively, are connected as shown in the figure. If galvanometer shows no deflection at the point $N$, the distance of point $N$ from the point $A$ is equal to
In the circuit shown in figure, potential difference between points $A$ and $B$ is $16\, V$. The current passing through $2\,\Omega $ resistance will be ................. $\mathrm{A}$
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________ $min$
The current in a conductor is expressed as $I=3 t^2+4 t^3$, where $I$ is in Ampere and $t$ is in second. The amount of electric charge that flows through a section of the conductor during $t=1$ s to $t=2 \mathrm{~s}$ is_______ C.
A cell, shunted by a $8 \; \Omega$ resistance, is balanced across a potentiometer wire of length $3 \; m$. The balancing length is $2 \; m$ when the cell is shunted by $4 \; \Omega$ resistance. The value of internal resistance of the cell will be $\dots \; \Omega .$
The number density of free electrons in copper is nearly $8 \times 10^{28}\,m ^{-3} . A$ copper wire has its area of cross section $=2 \times 10^{-6}\,m ^2$ and is carrying a current of $3.2\,A$. The drift speed of the electrons is $.....\times 10^{-6}\,ms ^{-1}$.
Forty electric bulbs are connected in series across a $220\, V$ supply. After one bulb is fused, the remaining $39$ are connected again in series across the same supply. The illumination will be
The supply voltage to room is $120\ V$. The resistance of the lead wires is $6\,\Omega$ . A $60\ W$ bulb is already switched on. What is the decrease of voltage across the bulb, when a $240\ W$ heater is switched on in parallel to the bulb? ............. $V$