What is the sum of the individual resistances in a series circuit equal to?

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Multiple Choice

What is the sum of the individual resistances in a series circuit equal to?

In a series circuit, the same current flows through every component, and the voltages across them add up to the total voltage. Using V = IR for each resistor with the same current, the total voltage is V_total = I(R1 + R2 + …). Since V_total is also I times the total resistance, R_total, you get R_total = R1 + R2 + …. So the sum of the individual resistances equals the total circuit resistance. This isn’t the voltage across a single resistor (that would be V_i = I*R_i), nor the current through the circuit (that current is the same through all components), and it’s not the power dissipated (P depends on I and R, not just a simple sum of resistances).

In a series circuit, the same current flows through every component, and the voltages across them add up to the total voltage. Using V = IR for each resistor with the same current, the total voltage is V_total = I(R1 + R2 + …). Since V_total is also I times the total resistance, R_total, you get R_total = R1 + R2 + …. So the sum of the individual resistances equals the total circuit resistance.

This isn’t the voltage across a single resistor (that would be V_i = I*R_i), nor the current through the circuit (that current is the same through all components), and it’s not the power dissipated (P depends on I and R, not just a simple sum of resistances).

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