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If the potential difference between the end of a wire of fixed resistance is doubled, by how much does the electric power increase?
- a)2 times
- b)3 times
- c)4 times
- d)1/2 times
- e)None of the above/More than one of the above
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If the potential difference between the end of a wire of fixed resist...
Electric power is defined as -
P=V2/R
Where, V = Potential difference
R = resistance
It is given that,
R is fixed and V becomes double
V ' = 2 V
Now, P' = (2V)2/R = 4 V2/R
P' = 4 (P)
So, the electric power becomes four times its previous value.
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Community Answer
If the potential difference between the end of a wire of fixed resist...
Understanding Electric Power
Electric power (P) in a circuit can be calculated using the formula:
P = V^2 / R
where:
- P is the power (in watts)
- V is the potential difference (in volts)
- R is the resistance (in ohms)
Impact of Doubling Potential Difference
When the potential difference (V) is doubled, we analyze the effect on power:
- New potential difference: 2V
- New power calculation:
P' = (2V)^2 / R
This expands to:
P' = 4V^2 / R
Comparing Old and New Power
Now, let's compare the original power (P) and the new power (P'):
- Original Power: P = V^2 / R
- New Power: P' = 4V^2 / R
To find the increase in power:
P' = 4 * (V^2 / R) = 4P
Conclusion
- The electric power increases by a factor of 4 when the potential difference is doubled.
- Hence, the correct answer is option 'C' - the power increases by 4 times.
This relationship highlights how sensitive electric power is to changes in voltage, emphasizing the quadratic nature of the formula.
Electric power (P) in a circuit can be calculated using the formula:
P = V^2 / R
where:
- P is the power (in watts)
- V is the potential difference (in volts)
- R is the resistance (in ohms)
Impact of Doubling Potential Difference
When the potential difference (V) is doubled, we analyze the effect on power:
- New potential difference: 2V
- New power calculation:
P' = (2V)^2 / R
This expands to:
P' = 4V^2 / R
Comparing Old and New Power
Now, let's compare the original power (P) and the new power (P'):
- Original Power: P = V^2 / R
- New Power: P' = 4V^2 / R
To find the increase in power:
P' = 4 * (V^2 / R) = 4P
Conclusion
- The electric power increases by a factor of 4 when the potential difference is doubled.
- Hence, the correct answer is option 'C' - the power increases by 4 times.
This relationship highlights how sensitive electric power is to changes in voltage, emphasizing the quadratic nature of the formula.
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If the potential difference between the end of a wire of fixed resistance is doubled, by how much does the electric power increase?a)2 timesb)3 timesc)4 timesd)1/2 timese)None of the above/More than one of the aboveCorrect answer is option 'C'. Can you explain this answer?
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