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In the circuit shown the resistance of voltmeter is $10,000\, ohm$ and that of ammeter is $20\,ohm$. The ammeter reading is $0.10\,Amp$ and voltmeter reading is $12$ $\mathrm{volt}.$ Then $R$ is equal to .............. $\Omega$
In the given figure, a battery of emf $E$ is connnected across a conductor $P Q$ of length $'Y'$ and different area of cross-sections having radii $r_{1}$ and $r_{2}\left(r_{2}\,<\,r_{1}\right)$.
Choose the correct option as one moves from $P$ to $Q$ :
A uniform heating wire of resistance $36\, \Omega$ is connected across a potential difference of $240\, {V}$ The wire is then cut into half and potential difference of $240\, {V}$ is applied across each half separately. The ratio of power dissipation in first case to the total power dissipation in the second case would be $1: {x}$, where ${x}$ is........... .