Question

Circuit 1 and circuit 2 consists of resistor $R_1$ and $R_2$ respectively. These resistors have same resistivity and thickness. Length of $R_1$ > length of $R_2$. If same voltage is applied across the circuits, which circuit has more current?

Answer 1

Resistance is directly proportional to the length of the wire as $R=\frac{\rho \times L}{A}$, where R is the resistance, L is the length of the wire, A is the area of the cross-section of wire and $\rho$ is the resistivity of the material. If the resistors have the same material and thickness than it implies that the resistors have same cross-sectional area and resistivity. Therefore resistance of these resistors is dependent only on the length of the wire. Hence, the resistance is greater in circuit 1 as the length of the resistor is more than in circuit 2. This means that the current is greater in circuit 2 than in circuit 1.