A constant voltage is applied between the two ends of a uniform metallic wire. Some heat is developed in it. The heat developed is double if
AIIMS 2012, Medium
Download our app for free and get started
$R=\frac{\rho \ell}{\pi r^{2}}$
When $\ell$ is $\frac{\ell}{2}$ and radius is $\frac{\mathrm{r}}{2}$
$\therefore \quad \mathrm{R}^{\prime}=\frac{\rho \ell{4}}{\pi 2 \mathrm{r}^{2}}=\frac{2 \rho \ell}{\pi \mathrm{r}^{2}}$
So, $\mathrm{R}^{\prime}=2 \mathrm{R}$ So, heat is doubled according to $\mathrm{H}=\mathrm{I}^{2} \mathrm{RT}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1The total power dissipated in watts in the circuit shown is ............. $W$View Solution
- 2A 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.......$V/cm$View Solution
- 3View SolutionThe resistance of a conductor increases with
- 4For comparing the $e.m.f.$'s of two cells with a potentiometer, a standard cell is used to develop a potential gradient along the wires. Which of the following possibilities would make the experiment unsuccessfulView Solution
- 5A potential $V_0$ is applied across a uniform wire of resistance $R$. The power dissipation is $P_1$. The wire is then cut into two equal halves and a potential of $V _0$ is applied across the length of each half. The total power dissipation across two wires is $P_2$. The ratio $P_2: P_1$ is $\sqrt{x}: 1$. The value of $x$ is $.............$.View Solution
- 6A meter bridge set up as shown to determine end correction at $A$ and $B$ . When a resistance of $15\,\Omega $ is used in left gap and of $20\,\Omega $ in right gap, then null point comes at a distance $42\ cm$ from $A$ . When these resistances are interchanged null point comes at a distance $57\ cm$ from $A$ . Values of end corrections areView Solution
- 7The reading of the ideal voltmeter in the adjoining diagram will be ................. $V$View Solution
- 8In 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.View Solution
- 9A battery of internal resistance $4$ $\Omega$ is connected to the network of resistances as shown. In order to give the maximum power to the network, the value of $R$ (in $\Omega $) should beView Solution
- 10A potentiometer is an accurate and versatile device to make electrical measurements of $EMF$ because the method involvesView Solution