Four equal resistors in parallel: With 15 V applied and a total equivalent resistance of 600 Ω, what is the current through each branch resistor?

Introduction / Context:Equal-value resistors in parallel have a simple relationship between the branch resistance and the equivalent resistance. This question checks your understanding of parallel networks and Ohm's law for branch currents.

Given Data / Assumptions:

• Total voltage across the network: 15 V.
• Four equal resistors in parallel.
• Total equivalent resistance R_eq = 600 Ω.

Concept / Approach:For N equal resistors, R_eq = R / N, so R = N * R_eq. Once the value of each resistor is known, the current in any branch is I_branch = V / R.

Step-by-Step Solution:

Verification / Alternative check:Total current I_total = V / R_eq = 15 / 600 = 0.025 A = 25 mA. For four equal branches, each carries 25 mA / 4 = 6.25 mA, confirming the result.

Why Other Options Are Wrong:

• 25 mA: That is the total current, not the current in one branch.
• 100 mA and 200 mA: Too large; would imply much smaller branch resistances.

Common Pitfalls:

• Mistaking total current for branch current in equal-parallel cases.
• Forgetting the N multiplier when recovering R from R_eq.

Final Answer:6.25 mA