Two wires $P$ and $Q$ are made of the same material. The wire $\mathbf{Q}$ has twice the diameter and half the length as that of wire $P$. If the resistance of wire $P$ is $R$, the resistance of the wire $Q$ will be

A battery supplies 0.9 A current through a $2 \Omega$ resistor and 0.3 A current through a $7 \Omega$ resistor when connected one by one. The internal resistance of the battery is

A galvanometer of resistance $50 \Omega$ is converted into a voltmeter of range $(0-2 \mathrm{~V})$ using a resistor of $1.0 \mathrm{k} \Omega$. If it is to be converted into a voltmeter of range ( $0-10 \mathrm{~V}$ ), the resistance required will be

A current of 0.8 A flows in a conductor of $$40 \Omega$$ for 1 minute. The heat produced in the conductor will be