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
- 1In steady state the potential difference across the capacitor is $10\,\, V.$ Each resistance is of $3\,\Omega $. The cell is ideal. The $emf$ of the cell is .............. $\mathrm{V}$View Solution
- 2A cube is formed with ten identical resistances $R$ (thick lines) and two shorting wires (dotted lines) along the arms $A C$ and $B D$ as shown in the figure below. Resistance between point $A$ and $B$ is ...........$\Omega$View Solution
- 3$100$ cells each of $e.m.f.$ $5\, V$ and internal resistance $1\, ohm$ are to be arranged so as to produce maximum current in a $25\, ohms$ resistance. Each row is to contain equal number of cells. The number of rows should beView Solution
- 4Find charge on the capacitor after $1$ sec of opening the switch at $t=\infty ?$View Solution
- 5In the circuit shown in figure, if ammeter and voltmeter are ideal, then the power consumed in $9 \,\Omega$ resistor will be .......... $W$View Solution
- 6In a balanced Wheatstone’s network, the resistances in the arms $Q$ and $S$ are interchanged. As a result of thisView Solution
- 7In a typical Wheatstone network, the resistances in cyclic order are $A = 10 \,\Omega $, $B = 5 \,\Omega $, $C = 4 \,\Omega $ and $D = 4 \,\Omega $ for the bridge to be balancedView Solution
- 8Four wires of the same diameter are connected in turn between two points, maintained at a constant potential difference. Their resistivities are; $\rho $ and $L$ (wire $1$ )., $1.2\,\rho $ and $1.2\,L$ (wire $2$ ), $0.9\,\rho $ and $0.9\,L$ (wire $3$ ) and $\rho $ and $1.5\,L$ (wire $4$ ). Rank the wires according to the rates at which energy is dissipated as heat, greatest firstView Solution
- 9The resistance of a wire of uniform diameter $d$ and length $L$ is $R$. The resistance of another wire of the same material but diameter $2d$ and length $4L$ will beView Solution
- 10In the circuit shown in figure, all cells are ideal. The current through $2 \,\Omega$ resistor is ............ $A$View Solution
