Which resistor in a DC series circuit has the greatest voltage drop if R1 = 25 ohms, R2 = 50 ohms, R3 = 75 ohms, and R4 = 10 ohms?

In a DC series circuit, the voltage drop across each resistor is determined by Ohm's Law, which states that the voltage drop (V) across a resistor is equal to the current (I) flowing through it multiplied by its resistance (R), expressed as V = I × R. Since all components are in series, the same current flows through each resistor, meaning the voltage drop across each resistor will differ based on its resistance value.

To find which resistor has the greatest voltage drop, you need to consider the resistance values. In the given scenario, R3 has the highest resistance at 75 ohms. Since the current is the same for each resistor in a series circuit, a higher resistance will result in a larger voltage drop across that resistor.

More specifically, the voltage drop for each resistor can be derived from their resistances: the resistor with the highest value will absorb a greater proportion of the total voltage supplied by the power source. Therefore, with R3 being 75 ohms, it will have the greatest voltage drop compared to the others, which are lower in resistance.

Thus, R3 is the correct answer since it has the greatest resistance and, consequently, the highest voltage drop in this DC series circuit.