In a series circuit, which two quantities are directly proportional?

In a series circuit, which two quantities are directly proportional?

• A. The current across the load and the value of the resistance of that load
• B. The current across the load and the voltage across the load
• C. The current and the wattage across that load
• D. The voltage across the load and the value of the resistance of that load

Answer: (D)

In a series circuit, the same current flows through every component. That current is I for the load, and Ohm’s law tells us the voltage across the load is V_load = I × R_load. Since the current is the same for that load, the voltage drop across it changes directly with the load’s resistance. If the resistance goes up, the voltage drop goes up in direct proportion; if the resistance goes down, the voltage drop goes down in direct proportion. So the voltage across the load and the resistance of that load are directly proportional. The other options don’t have this straightforward proportionality in a series circuit. The current through a load isn’t directly proportional to its own resistance because the overall circuit current depends on the total resistance and the source. While V = I R relates voltage, current, and resistance, the current varies with the circuit, so the pair that tracks changes together most directly is voltage across the load and its resistance. Wattage depends on both current and resistance (P = I^2 R), so it doesn’t line up with a simple direct proportionality to either quantity alone.

In a series circuit, the same current flows through every component. That current is I for the load, and Ohm’s law tells us the voltage across the load is V_load = I × R_load. Since the current is the same for that load, the voltage drop across it changes directly with the load’s resistance. If the resistance goes up, the voltage drop goes up in direct proportion; if the resistance goes down, the voltage drop goes down in direct proportion. So the voltage across the load and the resistance of that load are directly proportional.

The other options don’t have this straightforward proportionality in a series circuit. The current through a load isn’t directly proportional to its own resistance because the overall circuit current depends on the total resistance and the source. While V = I R relates voltage, current, and resistance, the current varies with the circuit, so the pair that tracks changes together most directly is voltage across the load and its resistance. Wattage depends on both current and resistance (P = I^2 R), so it doesn’t line up with a simple direct proportionality to either quantity alone.