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In a circuit with a 24V battery and three resistors (R1 = 4Ω, R2 = 4Ω, R3 = 4Ω)

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Question: In a circuit with a 24V battery and three resistors (R1 = 4Ω, R2 = 4Ω, R3 = 4Ω) in parallel, what is the total current supplied by the battery?

Options:

  1. 2A
  2. 3A
  3. 4A
  4. 6A

Correct Answer: 6A

Solution: 

Equivalent resistance R_eq = 1/(1/R1 + 1/R2 + 1/R3) = 1/(1/4 + 1/4 + 1/4) = 1.33Ω. Total current I = V/R_eq = 24V/1.33Ω = 18A.

In a circuit with a 24V battery and three resistors (R1 = 4Ω, R2 = 4Ω, R3 = 4Ω)

Practice Questions

Q1
In a circuit with a 24V battery and three resistors (R1 = 4Ω, R2 = 4Ω, R3 = 4Ω) in parallel, what is the total current supplied by the battery?
  1. 2A
  2. 3A
  3. 4A
  4. 6A

Questions & Step-by-Step Solutions

In a circuit with a 24V battery and three resistors (R1 = 4Ω, R2 = 4Ω, R3 = 4Ω) in parallel, what is the total current supplied by the battery?
Correct Answer: 18A
  • Step 1: Identify the values given in the problem. We have a 24V battery and three resistors, each with a resistance of 4Ω (R1, R2, R3).
  • Step 2: Since the resistors are in parallel, we need to find the equivalent resistance (R_eq) using the formula: R_eq = 1 / (1/R1 + 1/R2 + 1/R3).
  • Step 3: Substitute the values of the resistors into the formula: R_eq = 1 / (1/4 + 1/4 + 1/4).
  • Step 4: Calculate the sum inside the parentheses: 1/4 + 1/4 + 1/4 = 3/4.
  • Step 5: Now, take the reciprocal of 3/4: R_eq = 1 / (3/4) = 4/3 = 1.33Ω.
  • Step 6: Now that we have the equivalent resistance, we can find the total current (I) supplied by the battery using Ohm's Law: I = V / R_eq.
  • Step 7: Substitute the values into the formula: I = 24V / 1.33Ω.
  • Step 8: Calculate the total current: I ≈ 18A.
  • Parallel Resistor Calculation – Understanding how to calculate the equivalent resistance of resistors in parallel and applying Ohm's Law to find total current.
  • Ohm's Law – Applying the relationship between voltage, current, and resistance to determine the total current in a circuit.
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