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Two resistances equal at $0\,^oC$ with temperature coefficient of resistance $\alpha _1$ and $\alpha _2$ joined in series act as a single resistance in a circuit. The temperature coefficient of their single resistance will be
$A$ 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 given figure $R_1=10 \Omega, R_2=8 \Omega, R_3=4 \Omega$ and $R_4=8 \Omega$. Battery is ideal with emf $12 \mathrm{~V}$. Equivalent resistant of the circuit and current supplied by battery are respectively.
For driving a current of $2\, A$ for $6$ minutes in a circuit, $1000\, J$ of work is to be done. The $e.m.f.$ of the source in the circuit is ................ $V$
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
A parallel combination of two resistors, of $1 \,\Omega$ each, is connected in series with a $1.5 \,\Omega$ resistor. The total combination is connected across a $10\, V$ battery. The current flowing in the circuit is .............. $A$
Two cells of emf $E_1$ and $E_2\left(E_1 > E_2\right)$ are connected individually to a potentiometer and their corresponding balancing length are $625 \,cm$ and $500 \,cm$, then the ratio $\frac{E_1}{E_2}$ is ...........
Two resistance of $100\ \Omega$ and $200\ \Omega$ are connected in series with a battery of $4 \mathrm{~V}$ and negligible internal resistance. $A$ voltmeter is used to measure voltage across $100 \Omega$ resistance, which gives reading as $1 \mathrm{~V}$. The resistance of voltmeter must be ___$\Omega$.