If four equal resistors are connected in series to a supply, how is the power distributed among the resistors?

If four equal resistors are connected in series to a supply, how is the power distributed among the resistors?

• A. All resistors dissipate different amounts
• B. Only the first dissipates power
• C. Each resistor dissipates the same amount of power
• D. No power is dissipated

Answer: (C)

In a series circuit, the same current flows through every component. With four equal resistors, that current is identical for each resistor, and because each resistor has the same resistance, the voltage drop across each one is the same as well (V = I R). The power dissipated by a resistor is P = I^2 R. Since both the current and the resistance are the same for every resistor, each resistor wastes the same amount of power. The total power from the supply is shared equally, so each resistor dissipates one quarter of the total. This also matches P = V^2 / R when you note that the voltage across each resistor is one quarter of the supply voltage.

In a series circuit, the same current flows through every component. With four equal resistors, that current is identical for each resistor, and because each resistor has the same resistance, the voltage drop across each one is the same as well (V = I R). The power dissipated by a resistor is P = I^2 R. Since both the current and the resistance are the same for every resistor, each resistor wastes the same amount of power. The total power from the supply is shared equally, so each resistor dissipates one quarter of the total. This also matches P = V^2 / R when you note that the voltage across each resistor is one quarter of the supply voltage.