Question

The resistances 2Ω, 3Ω, and 5Ω are joined in series. If the two ends of the combination are joined to a potential difference of 30 volts, then find the potential difference between the ends of each resistance.

Hint:

In a series circuit, the sum of individual voltage drops equals the total supplied voltage.

Answer 1

In a series circuit, the same current flows through all resistors. Using Ohm’s law: \[ V = IR \] Total resistance: \[ R_{\text{total}} = 2 + 3 + 5 = 10Ω \] Total current: \[ I = \frac{V}{R_{\text{total}}} = \frac{30}{10} = 3A \] Voltage drop across each resistor: \[ V_1 = IR_1 = (3)(2) = 6V \] \[ V_2 = IR_2 = (3)(3) = 9V \] \[ V_3 = IR_3 = (3)(5) = 15V \] Thus, the potential differences across 2Ω, 3Ω, and 5Ω resistors are 6V, 9V, and 15V, respectively.