In a series circuit, what is true about currents and equivalent resistance?

In a series circuit, what is true about currents and equivalent resistance?

• A. Currents are equal; R_eq = R1 + R2
• B. Currents add; R_eq = R1 || R2
• C. Voltages are equal; R_eq = R1 + R2
• D. Currents are inversely proportional to voltages; R_eq = R1*R2/(R1+R2)

Answer: (A)

In a series circuit there is only one path for current, so the same current flows through every component. Because the current is the same through each resistor, you simply add their resistances to get the total or equivalent resistance: R_eq = R1 + R2. The voltage across the resistors shares the total supply voltage, not the current, so voltages can differ from one element to another even though the current is the same. The other statements mix up series and parallel behavior. In series, voltages are not all equal—larger resistances drop more voltage. Currents do not add in a single path; in series the current is constant through all components. The parallel formula for R_eq is not used in series; the correct series relationship is a sum of resistances.

In a series circuit there is only one path for current, so the same current flows through every component. Because the current is the same through each resistor, you simply add their resistances to get the total or equivalent resistance: R_eq = R1 + R2. The voltage across the resistors shares the total supply voltage, not the current, so voltages can differ from one element to another even though the current is the same.

The other statements mix up series and parallel behavior. In series, voltages are not all equal—larger resistances drop more voltage. Currents do not add in a single path; in series the current is constant through all components. The parallel formula for R_eq is not used in series; the correct series relationship is a sum of resistances.