A current of $5\; {A}$ is passing through a non-linear magnesium wire of cross-section $0.04\; {m}^{2}$. At every point the direction of current density is at an angle of $60^{\circ}$ with the unit vector of area of cross-section. The magnitude of electric field at every point of the conductor is ....${V} / {m}$ (Resistivity of magnesium is $\rho=44 \times 10^{-8}\, \Omega m$)
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Resistances ${R_1}$ and ${R_2}$ are joined in parallel and a current is passed so that the amount of heat liberated is ${H_1}$ and ${H_2}$ respectively. The ratio $\frac{{{H_1}}}{{{H_2}}}$ has the value
Potentiometer wire of length $1 \,m$ is connected in series with $490\,\Omega $ resistance and $2\,V$ battery. If $0.2\, mV/cm $ is the potential gradient, then resistance of the potentiometer wire is ................ $\Omega$
In the circuit shown in figure, the heat produced in $5\, ohm $ resistance is $10\, cal / sec$ . The heat produced in $4$ resistance is ................ $cal /sec$
Two electric bulbs whose resistance are in the ratio of $1: 2$, are connected in parallel to a constant voltage source. The power dissipated in them has the ratio
Resistances of $6\, ohm$ each are connected in the manner shown in adjoining figure. With the current $0.5\,ampere$ as shown in figure, the potential difference ${V_P} - {V_Q}$ is .............. $V$
$A$ 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 ............. $\Omega$
In the given figure, a battery of emf $E$ is connnected across a conductor $P Q$ of length $'Y'$ and different area of cross-sections having radii $r_{1}$ and $r_{2}\left(r_{2}\,<\,r_{1}\right)$.
Choose the correct option as one moves from $P$ to $Q$ :