What is immaterial for an electric fuse wire?

Two wires of thickness $1 \, mm$ and $2 \, mm$ have the same mass of copper. The two wires are connected in series and a current is passed through them. The ratio of the power generated in the wires will be ....

The battery in the diagram is to be charged by the generator $G$. The generator has a terminal voltage of $120 \ V$ when the charging current is $10 \ A$. The battery has an $emf$ of $100 \ V$ and an internal resistance of $1 \ \Omega$. In order to charge the battery at $10 \ A$ charging current,the resistance $R$ should be set at ................ $\Omega$.

The figure shows a network of resistors and a battery. If $1\,A$ current flows through the branch $CF$,then answer the following questions. The current through:

To determine the resistance $(R)$ of a wire,a circuit is designed as shown below. The $V-I$ characteristic curve for this circuit is plotted for the voltmeter and the ammeter readings as shown in the figure. The value of $R$ is . . . . . . . $\Omega$.

Three resistances $A, B$ and $C$ having values $3R, 6R$ and $R$ respectively form a network as shown. When a potential difference is applied across the network,the thermal powers dissipated by $A, B$ and $C$ are in the ratio: