## If the current I through a resistor is increased by 100% (assume that temperature remains unchanged), the increase in power dissipated will be

## (a) 100%

## (b) 200%

## (c) 300%

## (d) 400%

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Answer:
**

**
**

**
**

**
**

If current is ‘I’ and resistance is ‘R’, then power dissipated, P is:

**
P = I
**
^{
2
}
**
* R
**

If current is
**
increased by 100%
**
, then
**
current becomes 2I
**
.

Power dissipated when current is ‘2I’ and resistance is ‘R’, P’ is:

**
P’ = (2I)
**
^{
2
}
**
* R = 4I
**
^{
2
}
**
* R
**

Increase in power dissipated =
**
P’ - P
**

= 4I
^{
2
}
R - I
^{
2
}
R

**
= 3I
**
^{
2
}
**
R
**

**
% increase in power dissipated
**
= (increase in power dissipated / original power(P) ) * 100

= (3I
^{
2
}
R / I
^{
2
}
R ) * 100

= 3 * 100

=
**
300 %
**

So, the
**
correct answer is (c).
**