In the circuit shown in figure, the power which is dissipated as heat in the $6\,\Omega$ resistor is $6\,W$. What is the value of resistance $R$ in the circuit?................... $\Omega$

The same mass of copper is drawn into two wires $1\, mm$ and $2\, mm$ thick. Two wires are connected in series and current is passed through them. Heat produced in the wire is in the ratio

On an electric heater $220\, volt$ and $1100\, watt$ are marked. On using it for $4$ hours, the energy consumed in $kWh$ will be

Two bulbs of $(40 \;W, 200\; V)$ and $(100\; W, 200 \;V)$. Then correct relation for their resistance

The resistor of resistance '$R$' is connected to $25\, V$ supply and heat produced in it is $25\, J/sec$. The value of $R$ is .......... $\Omega $

Four wires of the same diameter are connected in turn between two points, maintained at a constant potential difference. Their resistivities are; $\rho $ and $L$ (wire $1$ )., $1.2\,\rho $ and $1.2\,L$ (wire $2$ ), $0.9\,\rho $ and $0.9\,L$ (wire $3$ ) and $\rho $ and $1.5\,L$ (wire $4$ ). Rank the wires according to the rates at which energy is dissipated as heat, greatest first