If a circuit has a 24V battery and two resistors of 6Ω and 12Ω in series, what is the voltage across the 12Ω resistor?

1 question

1 item

Q: If a circuit has a 24V battery and two resistors of 6Ω and 12Ω in series, what is the voltage across the 12Ω resistor?

Solution: Using the voltage divider rule, V2 = (R2 / (R1 + R2)) * Vtotal = (12 / (6 + 12)) * 24 = 16V.

Steps: 8

Step 1: Identify the total voltage from the battery, which is 24V.
Step 2: Identify the resistors in the circuit. We have R1 = 6Ω and R2 = 12Ω.
Step 3: Calculate the total resistance in the circuit by adding the two resistors together: Rtotal = R1 + R2 = 6Ω + 12Ω = 18Ω.
Step 4: Use the voltage divider rule to find the voltage across the 12Ω resistor (R2). The formula is V2 = (R2 / Rtotal) * Vtotal.
Step 5: Substitute the values into the formula: V2 = (12Ω / 18Ω) * 24V.
Step 6: Simplify the fraction: 12 / 18 = 2 / 3.
Step 7: Multiply by the total voltage: V2 = (2 / 3) * 24V = 16V.
Step 8: Conclude that the voltage across the 12Ω resistor is 16V.