A cell sends a current through a resistance $R$ for time $t$. Now the same cell sends current through another resistance $r$ for the same time. If same amount of heat is developed in both the resistance, then the internal resistance of cell is
Medium
Download our app for free and get started
(d)
$H_1=\frac{E^2 R}{\left(R+r_1\right)^2}$
$H_2=\frac{E^2 R}{\left(r+r_1\right)^2}$
$\frac{R}{\left(R+r_1\right)^2}=\frac{r}{\left(r+r_1\right)^2}$
$\frac{r+r_1}{R+r_1}=\frac{\sqrt{r}}{\sqrt{R}}$
$\sqrt{R} r_1+r \sqrt{R}=\sqrt{r} r_1+R \sqrt{r}$
$r_1(\sqrt{R}-\sqrt{r})=\sqrt{R r}(\sqrt{R}-\sqrt{r})$
$r_1=\sqrt{R r}$
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
- 1Consider the circuit shown in the figure. The current ${I_3}$ is equal toView Solution
- 2In the following circuit, the battery has an emf of $2\mathrm{V}$ and an internal resistance of $\frac{2}{3}\ \Omega$. The power consumption in the entire circuit is$..... W.$View Solution
- 3In the electric network shown, when no current flows through the $4\, \Omega $ resistor in the arm $EB$, the potential difference between the points $A$ and $D$ will be ............... $V$View Solution
- 4In a potentiometer, the null point is received at $7^{th}$ wire. If now we have to change the null point at $9^{th}$ wire, what should we do ?View Solution
- 5View SolutionIn the given circuit, with steady current, the potential drop across the capacitor must be
- 6In the circuit as shown in the figure, the heat produced by $6\, ohm$ resistance due to current flowing in it is $60$ calorie per second. The heat generated across $3\, ohm$ resistance per second will be ................. $calorie$View Solution
- 7View SolutionKirchhoff's second law is based on the law of conservation of
- 8A metal wire has a resistance of $35 \,\Omega$. If its length is increased to double by drawing it, then its new resistance will be (in $\Omega$)View Solution
- 9The three resistances $A, B$ and $C$ have values $3R, 6R$ and $R$ respectively. When some potential difference is applied across the network, the thermal powers dissipated by $A, B$ and $C$ are in the ratioView Solution
- 10We have a galvanometer of resistance $25\,\Omega $. It is shunted by a $2.5\,\Omega $ wire. The part of total current that flows through the galvanometer is given asView Solution