An electric bulb rated for $500 \mathrm{W}$ at $100 \mathrm{V}$ is used in a circuit having a $200 \mathrm{V}$ supply. The resistance $R$ that must be put in series with the bulb, so that the bulb draws $500 \mathrm{W}$ is:

The wiring of a house has resistance $6 \mathrm{\Omega }$. A $100 \mathrm{W}$ bulb is glowing. If a geyser of $1000 \mathrm{W}$ is switched on, the change in potential drop across the bulb is nearly:

In the following circuit, $5 \mathrm{\Omega }$ resistor develops $45 \mathrm{J} {\mathrm{s}}^{-1}$ due to current flowing through it. The power developed per second across $12 \mathrm{\Omega }$ resistor is:

A variable current flows through a $1 \mathrm{\Omega }$ resistor for $2$ $\mathrm{s}$. Time dependence of the current is shown in the graph.