In a meter bridge, the balancing length from the left end (standard resistance of $1 \,ohm$ is in the right gap) is found to be $20\, cm$. The value of the unknown resistance is ............... $\Omega$
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$A$ Wheatstone's bridge is balanced with a resistance of $625\, \Omega$ in the third arm, where $P, Q$ and $S$ are in the $1^{st}, 2^{nd}$ and $4^{th}$ arm respectively. If $P$ and $Q$ are interchanged, the resistance in the third arm has to be increased by $51\,\Omega$ to secure balance. The unknown resistance in the fourth arm is ............. $\Omega$
Four wires $AB,\,\,BC,\,\,CD,\,\,DA$ of resistance $4\, \Omega$ each and a fifth wire $BD$ of resistance $8\, \Omega$ are joined to form a rectangle $ABCD$ of which $BD$ is a diagonal. The effective resistance between the points $A$ and $B$ is
A potentiometer wire of length $L$ and a resistance $r$ are connected in series with a battery of e.m.f. $E_0$ and a resistance $r_1$. An unknown e.m.f. $E$ is balanced at a length $l$ of the potentiometer wire. The e.m.f. $E$ will be given by
Coefficient of linear expansion of material of resistor is $\alpha$. Its temperature coefficient of resistivity and resistance are $\alpha_\rho$ and $\alpha_R$ respectively, then correct relation is
A wire of resitance $R$ and length $L$ is cut into $5$ equal part. if these parts are joined parts are joined paralley, than result resistance will be:
In the circuit shown the cells are ideal and of equal emfs, the capacitance of the capacitor is $C$ and the resistance of the resistor is $R. X$ is first joined to $Y$ and then to $Z$. After a long time, the total heat produced in the resistor will be
The battery in the diagram is to be charged by the generator $G$. The generator has a terminal voltage of $120$ $\mathrm{volts}$ when the charging current is $10$ $\mathrm{amperes}.$ The battery has an $\mathrm{emf}$ of $100$ $\mathrm{volts}$ and an internal resistance of $1$ $\mathrm{ohm}.$ In order to charge the battery at $10$ $\mathrm{amperes}$ charging current, the resistance $R$ should be set at ................ $\Omega$
In given hollow cylindrical conductor current density is $J = \frac{J_0}{r^2}$ where $J_0$ is constant and $r$ is the distance from axis of cylinder. If radius of inner surface is $'a'$ and radius of outer surface is $2a$ then find current passed through the conductor.
The resistivity of iron is$1 \times {10^{ - 7}}\,ohm - m$. The resistance of a iron wire of particular length and thickness is $1\, ohm$. If the length and the diameter of wire both are doubled, then the resistivity in $ohm - m$ will be