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In a parallel circuit with three resistors of values 6 ohms, 3 ohms, and 2 ohms,

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Question: In a parallel circuit with three resistors of values 6 ohms, 3 ohms, and 2 ohms, what is the equivalent resistance?

Options:

  1. 1.5 ohms
  2. 2 ohms
  3. 2.5 ohms
  4. 3 ohms

Correct Answer: 2.5 ohms

Solution:

The formula for equivalent resistance in parallel is 1/R_eq = 1/R1 + 1/R2 + 1/R3. Thus, 1/R_eq = 1/6 + 1/3 + 1/2 = 1/6 + 2/6 + 3/6 = 6/6 = 1, so R_eq = 1 ohm.

In a parallel circuit with three resistors of values 6 ohms, 3 ohms, and 2 ohms,

Practice Questions

Q1
In a parallel circuit with three resistors of values 6 ohms, 3 ohms, and 2 ohms, what is the equivalent resistance?
  1. 1.5 ohms
  2. 2 ohms
  3. 2.5 ohms
  4. 3 ohms

Questions & Step-by-Step Solutions

In a parallel circuit with three resistors of values 6 ohms, 3 ohms, and 2 ohms, what is the equivalent resistance?
Correct Answer: 1 ohm
  • Step 1: Identify the values of the resistors in the parallel circuit. We have R1 = 6 ohms, R2 = 3 ohms, and R3 = 2 ohms.
  • Step 2: Write down the formula for equivalent resistance in a parallel circuit: 1/R_eq = 1/R1 + 1/R2 + 1/R3.
  • Step 3: Substitute the values of the resistors into the formula: 1/R_eq = 1/6 + 1/3 + 1/2.
  • Step 4: Convert each fraction to have a common denominator. The common denominator for 6, 3, and 2 is 6.
  • Step 5: Rewrite the fractions: 1/6 remains 1/6, 1/3 becomes 2/6, and 1/2 becomes 3/6.
  • Step 6: Add the fractions together: 1/6 + 2/6 + 3/6 = 6/6.
  • Step 7: Simplify the result: 6/6 = 1.
  • Step 8: Since 1/R_eq = 1, we find that R_eq = 1 ohm.
  • Equivalent Resistance in Parallel Circuits – Understanding how to calculate the total resistance in a circuit where components are connected in parallel.
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