A potentiometer having the potential gradient of $2\, mV/cm$ is used to measure the difference of potential across a resistance of $10 \,\Omega$. If a length of $50\, cm$ of the potentiometer wire is required to get the null point, the current passing through the $10 \,\Omega$ resistor is (in $mA$)
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A uniform heating wire of resistance $36\, \Omega$ is connected across a potential difference of $240\, {V}$ The wire is then cut into half and potential difference of $240\, {V}$ is applied across each half separately. The ratio of power dissipation in first case to the total power dissipation in the second case would be $1: {x}$, where ${x}$ is........... .
In the circuit shown in figure, the current drawn from the battery is $4\,A$. If $10 \,\Omega$ resistor is replaced by $20\,\Omega$ resistor, then current drawn from the circuit will be .............. $A$
Four resistances $10$ $\Omega$, $5$ $\Omega$, $7$ $\Omega$ and $3$ $\Omega$ are connected so that they form the sides of a rectangle $AB$, $BC$, $CD$ and $DA$ respectively. Another resistance of $10$ $\Omega$ is connected across the diagonal $AC$. The equivalent resistance between $A$ and $B $ is .............. $\Omega$
Following figures show different combinations of identical bulb$(s)$ connected to identical battery$(ies)$. Which option is correct regarding the total power dissipated in the circuit?
Two wires of equal diameters, of resistivities ${\rho _1}$ and ${\rho _2}$ and lengths $l_1$ and $l_2$, respectively, are joined in series. The equivalent resistivity of the combination is