What is the total resistance of a parallel circuit consisting of a 10 ohm branch and a 25 ohm branch?

What is the total resistance of a parallel circuit consisting of a 10 ohm branch and a 25 ohm branch?

• A. 8 ohms
• B. 10.3 ohms
• C. 7.0 ohms
• D. 7.14 ohms

Answer: (D)

To determine the total resistance of a parallel circuit, the formula used is: 1 / R_total = 1 / R1 + 1 / R2 where R1 and R2 are the resistances of the individual branches. In this case, one branch has a resistance of 10 ohms, and the other branch has a resistance of 25 ohms. Applying the values in the formula: 1 / R_total = 1 / 10 + 1 / 25 Finding a common denominator (which is 50), we rewrite the fractions: 1 / R_total = 5 / 50 + 2 / 50 This simplifies to: 1 / R_total = 7 / 50 To find R_total, take the reciprocal of both sides: R_total = 50 / 7 Calculating that gives approximately 7.14 ohms. This calculation accurately represents how the total resistance in a parallel circuit is determined, reflecting the fact that the total resistance will always be less than the smallest resistance in the circuit. Since the branches are in parallel, the total resistance decreases as more branches are added, leading to 7.14 ohms being the correct answer.

To determine the total resistance of a parallel circuit, the formula used is:

1 / R_total = 1 / R1 + 1 / R2

where R1 and R2 are the resistances of the individual branches. In this case, one branch has a resistance of 10 ohms, and the other branch has a resistance of 25 ohms.

Applying the values in the formula:

1 / R_total = 1 / 10 + 1 / 25

Finding a common denominator (which is 50), we rewrite the fractions:

1 / R_total = 5 / 50 + 2 / 50

This simplifies to:

1 / R_total = 7 / 50

To find R_total, take the reciprocal of both sides:

R_total = 50 / 7

Calculating that gives approximately 7.14 ohms.

This calculation accurately represents how the total resistance in a parallel circuit is determined, reflecting the fact that the total resistance will always be less than the smallest resistance in the circuit. Since the branches are in parallel, the total resistance decreases as more branches are added, leading to 7.14 ohms being the correct answer.