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Resistor Calculation in Parallel Circuit Answers and Explanation:

The problem asks you to find the resistance of resistor R1 in the circuit shown. The circuit consists of two resistors, R1 and R2, connected in parallel with a battery.

where Rt is the total resistance of the parallel combination, R1 is the resistance of the first resistor, and R2 is the resistance of the second resistor.

Step 2: Apply the formula to the given circuit

• Case 1: R1 decreases and R2 increases.

• Case 2: R1 and R2 both decrease.

From the formula for current in a parallel circuit:

I = V/Rt

1/Rt1 = 1/R1 + 1/R2 1/Rt2 = 1/R1 + 1/R2'

where R2' is the resistance of the second resistor.

I2/I1 = Rt1/Rt2

Rt1/Rt2 = 8.7 A / 5.8 A = 1.5

1.5 = Rt1/R1 + Rt1/R2

Rt1 = 1.5R1 + 1.5R2

I1 = V/Rt1

V = I1 * Rt1

8.7R1 + 531.9 ohms = 8.7 A * (1.5R1 + 91.5 ohms)

8.7R1 + 531.9 ohms = 13.05R1 + 798.9 ohms