Which statement describes Kirchhoff's Resistance Law for a series circuit?

Which statement describes Kirchhoff's Resistance Law for a series circuit?

• A. The total resistance in a series circuit is the product of the individual resistances.
• B. The total current in a series circuit equals the sum of currents through each component.
• C. The total voltage in a series circuit equals the sum of voltages across each component.
• D. The total resistance in a series circuit is the sum of the individual resistances.

Answer: (D)

In a series circuit, the total resistance is found by adding the individual resistances because the same current flows through every component. Since the current is constant, each resistor drops a voltage equal to V_i = I × R_i. The source voltage is the sum of all these drops: V_total = V_1 + V_2 + ... = I × (R_1 + R_2 + ...). Therefore, the equivalent resistance seen by the source is R_total = R_1 + R_2 + ... The idea that the total resistance is the product of resistances is incorrect because adding, not multiplying, these drops aligns with how voltages add when the current is the same through each element. In a series circuit, the current through each component is the same, so you don’t sum currents—the currents are equal. The statement about the total voltage being the sum of voltages across components is true for a series loop (that’s Kirchhoff’s Voltage Law), but it’s describing voltage behavior, not resistance.

In a series circuit, the total resistance is found by adding the individual resistances because the same current flows through every component. Since the current is constant, each resistor drops a voltage equal to V_i = I × R_i. The source voltage is the sum of all these drops: V_total = V_1 + V_2 + ... = I × (R_1 + R_2 + ...). Therefore, the equivalent resistance seen by the source is R_total = R_1 + R_2 + ...

The idea that the total resistance is the product of resistances is incorrect because adding, not multiplying, these drops aligns with how voltages add when the current is the same through each element. In a series circuit, the current through each component is the same, so you don’t sum currents—the currents are equal. The statement about the total voltage being the sum of voltages across components is true for a series loop (that’s Kirchhoff’s Voltage Law), but it’s describing voltage behavior, not resistance.