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If $n, e, \tau$ and $m$ are representing electron density, charge, relaxation time and mass of an electron respectively, then the resistance of a wire of length / and cross-sectional area $A$ is given by
Consider an electrical circuit containing a two way switch $^{\prime}{S}^{\prime}$. Initially ${S}$ is open and then ${T}_{1}$ is connected to ${T}_{2} .$ As the current in ${R}=6 \,\Omega$ attains a maximum value of steady state level, ${T}_{1}$ is disconnected from ${T}_{2}$ and immediately connected to ${T}_{3} .$ Potential drop across ${r}=3\, \Omega$ resistor immediately after $T_{1}$ is connected to $T_{3}$ is $....\,V.$ (Round off to the Nearest Integer)
A meter bridge is set-up as shown, to determine an unknown resistance ' $X$ ' using a standard $10$ ohm resistor. The galvanometer shows null point when tapping-key is at $52 \ cm$ mark. The end-corrections are $1 \ cm$ and $2 \ cm$ respectively for the ends $A$ and $B$. The determined value of ' $X$ ' is
A potentiometer wire of length $10 \,m$ and resistance$20 \,\Omega$ is connected in series with a $25 \,V$ battery and an external resistance $30\, \Omega$. A cell of emf $E$ in secondary circuit is balanced by $250\, cm$ long potentiometer wire. The value of $E$ (in volt) is $\frac{x}{10}$. The value of $x$ is.......
The ammeter $A$ reads $2\, A$ and the voltmeter $V$ reads $20\, V$. the value of resistance $R$ is (Assuming finite resistance's of ammeter and voltmeter)
A potentiometer wire of length $100\, cm$ has a resistance of $10\,\Omega $. It is connected in series with a resistance and a cell of $emf$ $2\, V$ and of negligible internal resistance. A source of $emf$ $10\,mV$ is balanced against a length of $40\, cm$ of the potentiometer wire. What is the value of external resistance ? .................. $\Omega$
To measure the internal resistance of a battery, potentiometer is used. For $\mathrm{R}=10 \Omega$, the balance point is observed at $\ell=500 \mathrm{~cm}$ and for $\mathrm{R}=1 \Omega$ the balance point is observed at $\ell=400 \mathrm{~cm}$. The internal resistance of the battery is approximately :