In the figure, the potentiometer wire $AB$ of length $L$ and resistance $9r$ is joined to the cell $D$ of $\mathrm{emf}$ $\varepsilon$ and internal resistance $r$. The cell $C’s$ $\mathrm{emf}$ is $\varepsilon /2$ and its internal resistance is $2r$. The galvanometer $G$ will show no deflection when the length $AJ$ is
Diffcult
Download our app for free and get started
Current through potentiometer $=\frac{\varepsilon}{r+9 r}=\frac{\varepsilon}{10 r}$
Potential difference across potentiometer $=i \times 9 r=V$
$=\frac{\varepsilon}{10 r} \times 9 r=V$
$\frac{9 \varepsilon}{10}=V$
Potential gradient $\frac{V}{L}=\frac{9 \varepsilon}{10 L}=\mathrm{K}$
For no deflection
$\frac{\varepsilon}{2}=k(A J)$
$\frac{\varepsilon}{2}=\frac{9 \varepsilon}{10 L} \times A J$
$\mathrm{AJ}=\frac{5}{9} L$
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
- 1There are $n$ similar conductors each of resistance $R$. The resultant resistance comes out to be $x$ when connected in parallel. If they are connected in series, the resistance comes out to beView Solution
- 2The variation of applied potential and current flowing through a given wire is shown in figure. The length of wire is $31.4 \,cm$. The diameter of wire is measured as $2.4 \,cm$. The resistivity of the given wire is measured as $x \times 10^{-3} \,\Omega cm$. The value of $x$ is_______ [Take $\pi=3.14]$View Solution
- 3The current between $B$ and $D$ in the given figure is .............. $amp$View Solution
- 4A voltmeter of resistance $1000\,\Omega$ is connected across a resistance of $500\, \Omega$ in the given circuit. What will be the reading of voltmeter .............. $V$View Solution
- 5Find the equivalent resistance between $P$ and $Q.$ (If each wire has a resistance $R$ )View Solution
- 6In the circuit shown below, a student performing Ohm's law experiment accidently puts the voltmeter and the ammeter as shown in the circuit below. The reading in the voltmeter will be close to .......... $V$View Solution
- 7View SolutionReading of ammeter in ampere for the following circuit is
- 8Every atom makes one free electron in copper. If $1.1$ $ampere$ current is flowing in the wire of copper having $1\, mm$ diameter, then the drift velocity (approx.) will be (Density of copper $ = 9 \times {10^3}\,kg\,{m^{ - 3}}$ and atomic weight = $63$)View Solution
- 9Voltmeter reads potential difference across the terminals of an old battery as $1.2\,volt$ , while a potentiometer reads $1.4\,volt$ . The internal resistance of battery is $40\,\Omega $ , then voltmeter resistance is .............. $\Omega$View Solution
- 10The resistance of a rectangular block of copper of dimensions $2 \,mm \times 2 \,mm \times 5 \,m$ between two square faces is $0.02 \,\Omega$. What is the resistivity of copper?View Solution