Find out the equivalent resistance between the points $a$ and $b$
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In the potentiometer circuit as shown in the figure, the balance length $Al = 60\ cm$ when switch $S$ is open. When switch $S$ is closed and the value of $R$ is $5W$ the balance length $Al' = 50 cm.$ The internal resistance of the cell $C'$ is : .............. $\Omega$
To measure the temperature coefficient of resistivity $\alpha$ of a semiconductor, an electrical arrangement shown in the figure is prepared. The arm BC is made up of the semiconductor. The experiment is being conducted at $25^{\circ} \mathrm{C}$ and resistance of the semiconductor arm is $3 \mathrm{~m} \Omega$. Arm BC is cooled at a constant rate of $2^{\circ} \mathrm{C} / \mathrm{s}$. If the galvanometer $\mathrm{G}$ shows no deflection after $10 \mathrm{~s}$, then $\alpha$ is :
Two wires of the same material are given. The first wire is twice as long as the second and has twice the diameter of the second. The resistance of the first will be
A potentiometer wire $PQ$ of $1\,m$ length is connected to a standard cell $E _{1}$. Another cell $E _{2}$ of emf $1.02\, V$ is connected with a resistance $'r'$ and switch $S$ (as shown in figure). With switch $S$ open, the null position is obtained at a distance of $49\, cm$ from $Q$. The potential gradient in the potentiometer wire is.......$V/cm$
The charge flowing through a resistance $R$ varies with time $t$ as $ Q=at-bt^2 $ where $a$ and $b$ are positive constants . The total heat produced in $R$ is