An unknown resistance $R_1$ is connected in series with a resistance of $10 \,\Omega$. This combinations is connected to one gap of a meter bridge while a resistance $R_2$ is connected in the other gap. The balance point is at $50\, cm$. Now, when the $10 \,\Omega$ resistance is removed the balance point shifts to $40\, cm$. The value of $R_1$ is (in $ohm$)
Medium
Download our app for free and get started
For first balancing condition $\frac{{10 + {R_1}}}{{{R_2}}} = \frac{{50}}{{50}}$
$ \Rightarrow $ ${R_2} = 10 + {R_1}$.
For second balancing condition
$\frac{{{R_1}}}{{{R_2}}} = \frac{{40}}{{60}}$ $ \Rightarrow $ $\frac{{{R_1}}}{{10 + {R_1}}} = \frac{2}{3}$
$ \Rightarrow $ ${R_1} = 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 thermo $e.m.f.$ of a thermo-couple is $25\,\mu V{/^o}C$ at room temperature. A galvanometer of $40\, ohm$ resistance, capable of detecting current as low as ${10^{ - 5}}\,A,$ is connected with the thermocouple. The smallest temperature difference that can be detected by this system is ................ $^oC$View Solution
- 2View SolutionA steel wire has a resistance twice that of an aluminium wire. Both of them are connected with a constant voltage supply. More heat will be dissipated in
- 3View SolutionAssertion : The electric bulbs glows immediately when switch is on.
Reason : The drift velocity of electrons in a metallic wire is very high.
- 4A battery is charged at a potential of $15\, V$ for $8$ hours when the current flowing is $10\, A$. The battery on discharge supplies a current of $5\, A$ for $15$ hours. The mean terminal voltage during discharge is $14\, V$. The "Watt-hour" efficiency of the battery is .............. $\%$View Solution
- 5Resistance of tungsten wire at $150\,^oC$ is $133\,\Omega $. Its resistance temperature coefficient is $0.0045\,^oC$. The resistance of this wire at $500\,^oC$ will be .............. $\Omega$View Solution
- 6Four resistances of $15\; \Omega, 12\; \Omega, 4 \;\Omega$ and $10\; \Omega$ respectively in cyclic order to form Wheats tone's network. The resistance that is to be connected in parallel with the resistance of $10\; \Omega$ to balance the network is .................. $\Omega$View Solution
- 7Five identical cells each of internal resistance $1\, \Omega$ and $emf \;5\, {V}$ are connected in series and in parallel with an external resistance $'R'.$ For what value of $'R',$ current in series and parallel combination will remain the same ? (in $\Omega$)View Solution
- 8An electric kettle takes $4\, A$ current at $220\, V$. How much time will it take to boil $1\, kg$ of water from room temperature $20\,^\circ C$ ? The temperature of boiling water is $100\,^\circ C$ .................. $minutes$View Solution
- 9$n$ equal cell having emf $E$ and internal resistance $r$, are connected in a circuit of a resistance $R$ . Same current flows in circuit either they are connected in series or parallel, ifView Solution
- 10View SolutionThe potentiometer is best for measuring voltage, as