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Circuit for the measurement of resistance by potentiometer is shown. The galvanometer is first connected at point $A$ and zero deflection is observed at length $P J = 10\ cm$ . In second case it is connected at point $C$ and zero deflection is observed at a length $30\ cm$ from $P$ . Then the unknown resistance $X$ is
The resistance of a wire is $20\, ohms$. It is so stretched that the length becomes three times, then the new resistance of the wire will be ............. $ohms$
Two cells are connected in opposition as shown. Cell $\mathrm{E}_1$ is of $8 \mathrm{~V}$ emf and $2 \ \Omega$ internal resistance; the cell $E_2$ is of $2 \mathrm{~V}$ emf and $4\ \Omega$ internal resistance. The terminal potential difference of cell $\mathrm{E}_2$ is:
Each element in the finite chain of resistors shown in the figure is $\,1\,\Omega $ . A current of $1\, A$ flows through the final element. Then what is the potential difference $V$ across input terminals of the chain .................. $\mathrm{volt}$
Two wires of same metal have the same length but their cross-sections are in the ratio $3:1$. They are joined in series. The resistance of the thicker wire is $10\,\Omega $. The total resistance of the combination will be ............. $\Omega$