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In the given circuit ' $a$ ' is an arbitrary constant. The value of $m$ for which the equivalent circuit resistance is minimum, will be $\sqrt{\frac{ x }{2}}$. The value of $x$ is ...........
Two $220\; V , 100 \;W$ bulbs are connected first in series and then in parallel. Each time the combination is connected to a $220 \;V \;AC$ supply line. The power drawn by the combination in each case respectively will be
In an electrical cable there is a single wire of radius $9\, mm$ of copper. Its resistance is $5\,\Omega $. The cable is replaced by $6$ different insulated copper wires, the radius of each wire is $3\,mm$. Now the total resistance of the cable will be ............... $\Omega$
The galvanometer deflection, when key $K_1$ is closed but $K_2$ is open, equals $\theta_0$ (see figure). On closing $K_2$ also and adjusting $R_2$ to $5\,\Omega $ , the deflection in galvanometer becomes $\frac{{\theta _0}}{5}$. The resistance of the galvanometer is, then, given by [Neglect the internal resistance of battery]: .................. $\Omega$
To verify Ohm's law, a student connects the voltmeter across the battery as, shown in the figure. The measured voltage is plotted as a function of the current, and the following graph is obtained If $V_0$ is almost zero, identify the correct statement