Two conductors made of the same material are connected across a common potential difference. Conductor $A$ has twice the diameter and twice the length of conductor $B$. The power delivered to the two conductors ${P_A}$ and ${P_B}$ respectively is such that ${P_A}/{P_B}$ equals to

If power in $3\,\Omega $ is $27\,W$ then what is the power in $2\,\Omega $  ................ $\mathrm{W}$

In the figure shown the power generated in $y$ is maximum when $y = 5\,\Omega$ . Then $R$ is .............. $\Omega$

Assertion : Long distance power transmission is done at high voltage.

Reason : At high voltage supply power losses are less.

Heat produced in a wire of resistance $R$ due to current flowing at constant potential difference is proportional to

A potential $V_0$ is applied across a uniform wire of resistance $R$. The power dissipation is $P_1$. The wire is then cut into two equal halves and a potential of $V _0$ is applied across the length of each half. The total power dissipation across two wires is $P_2$. The ratio $P_2: P_1$ is $\sqrt{x}: 1$. The value of $x$ is $.............$.