Two resistors R1 and R2 are connected in series to a battery with no internal resistance. The current through each is measured. A third resistor, R3, is then connected in parallel to R2. How does this affect the currents throughR1 and R2?Question 58 Answer Choices A. I1 and I2 both increase. B. I1 increases and I2 decreases. C. I1 decreases and I2 increases. D. I1 and I2 both decrease.
Question
Two resistors R1 and R2 are connected in series to a battery with no internal resistance. The current through each is measured. A third resistor, R3, is then connected in parallel to R2. How does this affect the currents throughR1 and R2?Question 58 Answer Choices A. I1 and I2 both increase. B. I1 increases and I2 decreases. C. I1 decreases and I2 increases. D. I1 and I2 both decrease.
Solution
The correct answer is B. I1 increases and I2 decreases.
Here's why:
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When R3 is added in parallel to R2, the total resistance of the circuit decreases. This is because the total resistance of resistors in parallel is less than the smallest resistance in the group.
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According to Ohm's law (V = IR), if the resistance decreases and the voltage remains constant (which it does, because the battery has no internal resistance), the total current (I) in the circuit must increase.
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The total current flows through R1, so the current through R1 (I1) increases.
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However, now that R2 and R3 are in parallel, they share the increased total current. Even though the total current has increased, the current through R2 (I2) decreases because some of the current is now also flowing through R3.
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