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In india electricity is supplied for domestic use at $220\,\,V$. It is supplied at $110\,\, V$ in $USA$. If resistance of $60\,\, W$ bulb for use in India is $R$, then the resistance of $60\,\, W$ bulb for use in $USA$ will be
An ideal battery of $4\, V$ and resistance $R$ are connected in series in the primary circuit of a potentiometer of length $1\, m$ and resistance $5\,\Omega $ . The value of $R$, to give a difference of $5\, mV$ across $10\, cm$ of potentiometer wire, is: ................ $\Omega$
A battery of internal resistance one ohm and $emf$ $3\,volt$ sends a current through $1\,metre$ of uniform wire of resistance $5\,\Omega $. The pole of the cell of $emf$ $1.4\,volt$ are connected to two points on the wire so that no current passes through this cell. Then, the potential gradient of the wire is
Two students $P$ and $Q$ perform an experiment to verify Ohm's law for a conductor with resistance $R$. They use a current source and a voltmeter with least counts of $0.1 mA$ and $0.1 \,mV$, respectively. The plots of the variation of voltage drop $V$ across $R$ with current $I$ for both are shown below. The statement which is most likely to be correct?
At room temperature $\left(27^{\circ} \mathrm{C}\right)$, the resistance of a heating element is $50 \Omega$. The temperature coefficient of the material is $2.4 \times 10^{-4}{ }^{\circ} \mathrm{C}^1$. The temperature of the element, when its resistance is $62 \Omega$, is $\qquad$ ${ }^{\circ} \mathrm{C}$.
The thermo $e.m.f.$ of a thermo-couple is $25\,\mu V{/^o}C$ at room temperature. A galvanometer of $40\, ohm$ resistance, capable of detecting current as low as ${10^{ - 5}}\,A,$ is connected with the thermocouple. The smallest temperature difference that can be detected by this system is ................ $^oC$
In the following circuit, $18\,\Omega $ resistor develops $2\,J/sec$ due to current flowing through it. The power developed across $10\,\Omega $ resistance is .............. $W$
The current $i_1$ and $i_2$ through the resistor $R_1 (= 10\,\Omega )$ and $R_2 (=30 \,\Omega )$ in the circuit diagram with $E_1 = 3\,V, E_2 = 3\,V$ and $E_3 = 2\,V$ are respectively: