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Using Kirchhoff's Voltage Law, if a loop in a circuit has a 12V battery and two

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Question: Using Kirchhoff\'s Voltage Law, if a loop in a circuit has a 12V battery and two resistors of 4Ω and 6Ω, what is the voltage drop across the 4Ω resistor?

Options:

  1. 4.8V
  2. 8V
  3. 6V
  4. 3.2V

Correct Answer: 8V

Solution: 

Using voltage division, V_R1 = V_total * (R1 / (R1 + R2)) = 12V * (4Ω / (4Ω + 6Ω)) = 12V * (4/10) = 4.8V.

Using Kirchhoff's Voltage Law, if a loop in a circuit has a 12V battery and two

Practice Questions

Q1
Using Kirchhoff's Voltage Law, if a loop in a circuit has a 12V battery and two resistors of 4Ω and 6Ω, what is the voltage drop across the 4Ω resistor?
  1. 4.8V
  2. 8V
  3. 6V
  4. 3.2V

Questions & Step-by-Step Solutions

Using Kirchhoff's Voltage Law, if a loop in a circuit has a 12V battery and two resistors of 4Ω and 6Ω, what is the voltage drop across the 4Ω resistor?
  • Step 1: Identify the total voltage in the circuit, which is given as 12V from the battery.
  • Step 2: Identify the resistors in the circuit. We have R1 = 4Ω and R2 = 6Ω.
  • Step 3: Calculate the total resistance in the circuit by adding the two resistors: R_total = R1 + R2 = 4Ω + 6Ω = 10Ω.
  • Step 4: Use the voltage division formula to find the voltage drop across the 4Ω resistor (R1). The formula is V_R1 = V_total * (R1 / R_total).
  • Step 5: Substitute the values into the formula: V_R1 = 12V * (4Ω / 10Ω).
  • Step 6: Simplify the fraction: 4Ω / 10Ω = 0.4.
  • Step 7: Multiply to find the voltage drop: V_R1 = 12V * 0.4 = 4.8V.
  • Kirchhoff's Voltage Law – This law states that the sum of the electrical potential differences (voltage) around any closed network is zero.
  • Voltage Division – A technique used to determine the voltage drop across a resistor in a series circuit based on the total voltage and the resistances.
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