A $3\,^oC$ rise in temperature is observed in a conductor by passing a certain current. When the current is doubled, the rise in temperature will be ............. $^oC$

Pick out the wrong statement

Two identical batteries, each of $e.m.f.$ $2\, volt$ and internal resistance $1.0\, ohm$ are available to produce heat in an external resistance $R = 0.5\,ohm$ by passing a current through it. The maximum Joulean power that can be developed across $R$ using these batteries is ............. $watt$

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 $.............$.

You are given a resistance wire of length $50\, cm$ and a battery of negligible resistance. In which of the following cases is largest amount of heat generated

A resistor develops $500\, J$ of thermal energy in $20 \,s$ when a current of $1.5\, A$ is passed through it. If the current is increased from $1.5 \,A$ to $3\, A$ what will be the energy (in $J$) developed in $20\, s$.