Four wires are made of the same highly resistive material, cut to the same length, and connected in series. Wire 1 has resistanc
e R1 and cross-sectional area A. Wire 2 has resistance R2 and cross-sectional area 2A. Wire 3 has resistance R3 and cross-sectional area 3A. Wire 4 has resistance R4 and cross-sectional area 4A. A voltage V0 is applied across the series, as shown in the figure.Find the voltage V2 across wire 2.Give your answer in terms of V0, the voltage of the battery.
The 4 wires are connected in series: this means that the same current flow through them, and the voltage of the battery, V0, is equal to the sum of the voltages on each individual resistor:
Also, the equivalent resistance of the series circuit is
The voltage V2 across wire 2 is given by Ohm's law:
(1)
where I is the total current in the circuit, which is given by:
Substituting this into eq. (1), we find an expression for V2: