3. Two resistors of the same resistance, first connected in series combination, and then connected in parallel combination. What is the percentage change in the current in the circuit from series to parallel combinations if the same battery is used in both the cases? (5 marks)
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Answer:
So, the percentage change in the current in the circuit when changing from series to parallel combination is an increase of 300%.
Explanation:
The percentage change in current when two resistors are connected in series and then in parallel can be calculated using Ohm's law.
Let's assume the resistance of each resistor is "R" ohms, and the voltage of the battery is "V" volts.
1. **Series Combination:**
In series, the total resistance is the sum of the individual resistances, so the equivalent resistance is 2R. Using Ohm's law, the current (I1) in the circuit is given by:
I1 = V / (2R)
2. **Parallel Combination:**
In parallel, the equivalent resistance (Rp) is given by:
1/Rp = 1/R + 1/R = 2/R
Rp = R/2
Using Ohm's law, the current (I2) in the circuit is given by:
I2 = V / (R/2) = 2V / R
Now, let's calculate the percentage change in current:
Percentage Change = [(I2 - I1) / I1] * 100
Percentage Change = [(2V/R - V/(2R)) / (V/(2R))] * 100
Percentage Change = [(4 - 1) / 1] * 100
Percentage Change = 300%
So, the percentage change in the current in the circuit when changing from series to parallel combination is an increase of 300%.
Answer:
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