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I is the current passing through a circular wire. If the radius of the wire is changed to twice, then what will be the current passing through the wire?
- a)2I
- b)4I
- c)I/2
- d)I/4
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
I is the current passing through a circular wire. If the radius of the...
Current, I = V/R
If the radius becomes twice, the area becomes 4 times and resistance becomes R/4, as resistance is inversely proportional to the area of wire.
New current = 4V/R = 4I
If the radius becomes twice, the area becomes 4 times and resistance becomes R/4, as resistance is inversely proportional to the area of wire.
New current = 4V/R = 4I
Most Upvoted Answer
I is the current passing through a circular wire. If the radius of the...
Explanation:
When the radius of the wire is changed, the current passing through the wire is affected due to the change in the wire's cross-sectional area.
Key Points:
- The current passing through a wire is directly proportional to the cross-sectional area of the wire.
- When the radius of a wire is doubled, the cross-sectional area of the wire becomes four times.
- The current passing through the wire is inversely proportional to the cross-sectional area. Hence, when the cross-sectional area increases, the current passing through the wire decreases.
Calculation:
Let's assume the initial current passing through the wire is I. When the radius of the wire is changed to twice, the new radius becomes 2r.
The formula for the cross-sectional area of a circle is given by:
A = πr^2
Initially, the cross-sectional area of the wire is A = πr^2. When the radius is changed to 2r, the new cross-sectional area becomes:
A' = π(2r)^2 = 4πr^2
As we can see, the new cross-sectional area is four times the initial cross-sectional area.
According to the key points mentioned earlier, the current passing through the wire is inversely proportional to the cross-sectional area. Therefore, when the cross-sectional area increases by four times, the current passing through the wire decreases by four times.
So, the current passing through the wire when the radius is changed to twice is 4I.
Hence, the correct answer is option B) 4I.
When the radius of the wire is changed, the current passing through the wire is affected due to the change in the wire's cross-sectional area.
Key Points:
- The current passing through a wire is directly proportional to the cross-sectional area of the wire.
- When the radius of a wire is doubled, the cross-sectional area of the wire becomes four times.
- The current passing through the wire is inversely proportional to the cross-sectional area. Hence, when the cross-sectional area increases, the current passing through the wire decreases.
Calculation:
Let's assume the initial current passing through the wire is I. When the radius of the wire is changed to twice, the new radius becomes 2r.
The formula for the cross-sectional area of a circle is given by:
A = πr^2
Initially, the cross-sectional area of the wire is A = πr^2. When the radius is changed to 2r, the new cross-sectional area becomes:
A' = π(2r)^2 = 4πr^2
As we can see, the new cross-sectional area is four times the initial cross-sectional area.
According to the key points mentioned earlier, the current passing through the wire is inversely proportional to the cross-sectional area. Therefore, when the cross-sectional area increases by four times, the current passing through the wire decreases by four times.
So, the current passing through the wire when the radius is changed to twice is 4I.
Hence, the correct answer is option B) 4I.
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I is the current passing through a circular wire. If the radius of the wire is changed to twice, then what will be the current passing through the wire?a)2Ib)4Ic)I/2d)I/4Correct answer is option 'B'. Can you explain this answer?
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