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The total resistance of a circuit having two parallel resistors is 1.403 kilo-ohm. If one of the resistors is 2.0 kilo-ohm then the other resistor will be
- a)1.403 kilo-ohm
- b)2.0 kilo-ohm
- c)3.403 kilo-ohm
- d)4.70 kilo-ohm
- e)None of the above / More than one of the above
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The total resistance of a circuit having two parallel resistors is 1.4...
The correct answer is 4.70 kilo-ohm.
Solution:
- Total Resistance (R) = 1.403 kilo-ohm.
- R1 = 2.0 Kilo-ohm.
- R2 =?
- 1 kilo-ohm = 103 ohm.
- 1.403 kilo-ohm = 1403 ohm.
- 2 kilo-ohm = 2000 ohm.
- Now, for parallel combination:
- 1/R = 1/R1 + 1/R2
- On putting the values; 1/1403 = 1/2000 + 1/ R2
- 1/1043 - 1/2000 = R2
- 2000 - 1403 / 1403 x 2000 = 1/R2
- 597/ 1403 x 2000 = 1/R2
- R2 = 1403 x 2000 / 597 = 2806000 / 597 = 4700.16
- R2 = 4700.16 ohm
- If 103 ohm = 1 kilo-ohm
- then, 4700 ohm = 4.7 kilo-ohm
- Therefore, R2 = 4.7 kilo-ohm.
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Community Answer
The total resistance of a circuit having two parallel resistors is 1.4...
Total Resistance in Parallel Resistors
When two resistors are connected in parallel, the total resistance (R_total) can be calculated using the formula:
1/R_total = 1/R1 + 1/R2
Where:
- R_total is the total resistance of the parallel resistors.
- R1 is the resistance of the first resistor.
- R2 is the resistance of the second resistor.
In this case:
Given Values
- R_total = 1.403 kilo-ohms
- R1 = 2.0 kilo-ohms
Finding the Unknown Resistance (R2)
Using the formula, we can rearrange it to find R2:
1/R2 = 1/R_total - 1/R1
Substituting the Values
1/R2 = 1/1.403 - 1/2.0
Calculating Each Component
- 1/1.403 ≈ 0.712
- 1/2.0 = 0.5
Combine the Results
1/R2 = 0.712 - 0.5 = 0.212
Calculating R2
R2 = 1 / 0.212 ≈ 4.70 kilo-ohms
Conclusion
Therefore, the resistance of the other resistor (R2) is approximately 4.70 kilo-ohms. Thus, the correct answer is option 'D'.
- This shows that when one resistor is significantly lower in resistance, the equivalent resistance in parallel is reduced, leading to a larger resistance in the other resistor to maintain the total resistance of 1.403 kilo-ohms.
When two resistors are connected in parallel, the total resistance (R_total) can be calculated using the formula:
1/R_total = 1/R1 + 1/R2
Where:
- R_total is the total resistance of the parallel resistors.
- R1 is the resistance of the first resistor.
- R2 is the resistance of the second resistor.
In this case:
Given Values
- R_total = 1.403 kilo-ohms
- R1 = 2.0 kilo-ohms
Finding the Unknown Resistance (R2)
Using the formula, we can rearrange it to find R2:
1/R2 = 1/R_total - 1/R1
Substituting the Values
1/R2 = 1/1.403 - 1/2.0
Calculating Each Component
- 1/1.403 ≈ 0.712
- 1/2.0 = 0.5
Combine the Results
1/R2 = 0.712 - 0.5 = 0.212
Calculating R2
R2 = 1 / 0.212 ≈ 4.70 kilo-ohms
Conclusion
Therefore, the resistance of the other resistor (R2) is approximately 4.70 kilo-ohms. Thus, the correct answer is option 'D'.
- This shows that when one resistor is significantly lower in resistance, the equivalent resistance in parallel is reduced, leading to a larger resistance in the other resistor to maintain the total resistance of 1.403 kilo-ohms.
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The total resistance of a circuit having two parallel resistors is 1.403 kilo-ohm. If one of the resistors is 2.0 kilo-ohm then the other resistor will bea)1.403 kilo-ohmb)2.0 kilo-ohmc)3.403 kilo-ohmd)4.70 kilo-ohme)None of the above / More than one of the aboveCorrect answer is option 'D'. Can you explain this answer?
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