Two resistors 8 Ω and 2 Ω are in series across a 20 V source. What is the current, and the voltage across each resistor?

Two resistors 8 Ω and 2 Ω are in series across a 20 V source. What is the current, and the voltage across each resistor?

• A. I = 1 A; V8 = 8 V; V2 = 12 V
• B. I = 2 A; V8 = 16 V; V2 = 4 V
• C. I = 4 A; V8 = 32 V; V2 = -12 V
• D. I = 0.5 A; V8 = 4 V; V2 = 16 V

Answer: (B)

In a series circuit, the same current flows through every component, and the voltages add up to the total supply with the share of each resistor proportional to its resistance. The total resistance is 8 Ω + 2 Ω = 10 Ω, so the current from a 20 V source is I = 20 V / 10 Ω = 2 A. This current is the same through both resistors. The 8 Ω resistor drops V8 = I × 8 Ω = 2 A × 8 Ω = 16 V, and the 2 Ω resistor drops V2 = I × 2 Ω = 2 A × 2 Ω = 4 V. The voltages add to 16 V + 4 V = 20 V, matching the source. So the current is 2 A, with 16 V across the 8 Ω resistor and 4 V across the 2 Ω resistor.

In a series circuit, the same current flows through every component, and the voltages add up to the total supply with the share of each resistor proportional to its resistance. The total resistance is 8 Ω + 2 Ω = 10 Ω, so the current from a 20 V source is I = 20 V / 10 Ω = 2 A. This current is the same through both resistors. The 8 Ω resistor drops V8 = I × 8 Ω = 2 A × 8 Ω = 16 V, and the 2 Ω resistor drops V2 = I × 2 Ω = 2 A × 2 Ω = 4 V. The voltages add to 16 V + 4 V = 20 V, matching the source. So the current is 2 A, with 16 V across the 8 Ω resistor and 4 V across the 2 Ω resistor.