A fan motor is in series with a resistor. The resistor gets hot when the motor is running. The voltage drops across the motor and resistor will read:

• A. in proportion to the resistance of each load
• B. equal across both
• C. proportional to current
• D. independent of resistance

Answer: (A)

In a series circuit the same current flows through every component, so the voltage drop across each part depends on its resistance. The drop across the motor is V_motor = I × R_motor and the drop across the resistor is V_resistor = I × R_resistor. Because the current is the same, the voltages are proportional to their resistances: the larger the resistance, the larger the share of the supply voltage it gets. The resistor heating up is a reminder that it’s dissipating power P = I²R, which increases with resistance at the same current. So the readings across the motor and the resistor will be in proportion to their resistances.