Resistance are connected in a meter bridge circuit as shown in the figure. The balancing length $l_{1}$ is $40\,cm$. Now an unknown resistance $x$ is connected in series with $P$ and new balancing length is found to be $80\,cm$ measured from the same end. Then the value of $x$ will be $.......\Omega$
JEE MAIN 2022, Diffcult
Download our app for free and get started
Initially, $\frac{ P }{ Q }=\frac{40 cm }{60 cm }=\frac{2}{3}$
Finally, $\frac{ P + x }{ Q }=\frac{80 cm }{20 cm }=\frac{4}{1} \ldots(2)$
Divide $(2)$ by $(1)$
$\frac{ P + x }{ P }=4 \times \frac{3}{2}=6$
$1+\frac{ x }{ P }=6 \Rightarrow \frac{ x }{ P }=5$
$\therefore x =5 P =5 \times 4=20 \Omega$
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 ratio of heat dissipated per second through the resistance $5 \Omega$ and $10 \Omega$ in the circuit given below is: :View Solution
- 2A current of $1.6\, A$ is flowing through a wire having cross-sectional area $1\, mm^2$. If density of free electrons in the material of the wire is $10^{29}\, per\, m^3$, the drift velocity of electrons will beView Solution
- 3If a power of $100\, W$ is being supplied across a potential difference of $200\, V$, current flowing is ............ $A$View Solution
- 4A current i passes through a wire of length $l$, radius of cross-section $r$ and resistivity $\rho$. The rate of heat generation isView Solution
- 5In the arangement of resistances shown below, the effective resistance between points $A$ and $B$ is ............... $\Omega$View Solution
- 6The resistance per centimeter of a meter bridge wire is $\mathrm{r}$, with $\mathrm{X}\ \Omega$ resistance in left gap. Balancing length from left end is at $40 \mathrm{~cm}$ with $25\ \Omega$ resistance in right gap. Now the wire is replaced by another wire of $2 \mathrm{r}$ resistance per centimeter. The new balancing length for same settings will be atView Solution
- 7In the given figure, the charge stored in $6 \ \mu \mathrm{F}$ capacitor, when points $A$ and $B$ are joined by a connecting wire is___________ $\mu \mathrm{C}$.View Solution
- 8A parallel combination of two resistors, of $1 \,\Omega$ each, is connected in series with a $1.5 \,\Omega$ resistor. The total combination is connected across a $10\, V$ battery. The current flowing in the circuit is .............. $A$View Solution
- 9For 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
- 10In the figure shown, the total resistance between $A$ and $B$ is ............. $\Omega$View Solution
