In a circuit with a 24V battery and two resistors in series (4Ω and 8Ω), what is

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Question: In a circuit with a 24V battery and two resistors in series (4Ω and 8Ω), what is the voltage across the 8Ω resistor?

Options:

Correct Answer: 12V

Solution:

Voltage across 8Ω resistor = (R2 / (R1 + R2)) * Vtotal = (8 / (4 + 8)) * 24 = 16V.

In a circuit with a 24V battery and two resistors in series (4Ω and 8Ω), what is the voltage across the 8Ω resistor?

In a circuit with a 24V battery and two resistors in series (4Ω and 8Ω), what is the voltage across the 8Ω resistor?

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

Voltage Division – The principle that the voltage across a resistor in a series circuit is proportional to its resistance relative to the total resistance.
Ohm's Law – The relationship between voltage, current, and resistance in an electrical circuit, expressed as V = IR.