First slide

Ohm's law

Question

In India electricity is supplied for domestic use at 220V. It is supplied at 110 V in USA. If the resistance of a 60 W bulb for use in India is R, the resistance of a 60 W bulb for use in USA will be :

Moderate

A

2 R
B

$\frac{R}{4}$
C

$\frac{R}{2}$
D

R

Solution

$R_{AB} = \frac{ρ (\frac{l}{2})}{π {(2 r)}^{2}} = \frac{ρl}{8 {πr}^{2}}, R_{BC} = \frac{ρ (\frac{l}{2})}{π {(r)}^{2}} = \frac{ρl}{2 {πr}^{2}}$
$\Rightarrow R_{BC} = 4 R_{AB}$
Both are connected in series so $V_{BC} = 4 V_{AB}$
Also, $\frac{P_{BC}}{P_{AB}} = \frac{I^{2} R_{BC}}{I^{2} R_{AB}} = 4$

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