Question

If the current in a heater increases by 10 percent the percentage change in the power consumption

Answer 1

Answer:

The change in the power consumption is 21 %.

Explanation:

Given that,

If the current in a heater increases by 10 percent.

$I'=\dfrac{10I+I}{100}$

$I'=1.1I$

We need to calculation the power consumption

Using formula of power

$P\propto I^2$...(I)

$P'\propto I'^2$...(II)

From equation (I) and (II)

$\dfrac{P}{P'}=\dfrac{I^2}{I'^2}$

$\dfrac{P}{P'}=\dfrac{I^2}{(1.1I)^2}$

$\dfrac{P}{P'}=\dfrac{I^2}{1.21I^2}$

$P'=1.21P$

We need to calculate the change in the power consumption

$\dfrac{P'-P}{P}\times100=\dfrac{0.21P}{P}\times100$

$\dfrac{P'-P}{P}\times100=21\%$

Hence, The change in the power consumption is 21 %.

Answer 2

Answer:

Answer:

The change in the power consumption is 21 %.

Explanation:

Given that,

If the current in a heater increases by 10 percent.

I'=\dfrac{10I+I}{100}I

′

=

100

10I+I

I'=1.1II

′

=1.1I

We need to calculation the power consumption

Using formula of power

P\propto I^2P∝I

2

...(I)

P'\propto I'^2P

′

∝I

′2

...(II)

From equation (I) and (II)

\dfrac{P}{P'}=\dfrac{I^2}{I'^2}

P

′

P

=

I

′2

I

2

\dfrac{P}{P'}=\dfrac{I^2}{(1.1I)^2}

P

′

P

=

(1.1I)

2

I

2

\dfrac{P}{P'}=\dfrac{I^2}{1.21I^2}

P

′

P

=

1.21I

2

I

2

P'=1.21PP

′

=1.21P

We need to calculate the change in the power consumption

\dfrac{P'-P}{P}\times100=\dfrac{0.21P}{P}\times100

P

P

′

−P

×100=

P

0.21P

×100

\dfrac{P'-P}{P}\times100=21\%

P

P

′

−P

×100=21%

Hence, The change in the power consumption is 21 %.