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An electric bulb is rated as $200 V - 100 W$ . What is its resistance?

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100 Ohms

200 Ohms

300 Ohms

400 Ohms

answer is D.

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Detailed Solution

The resistance of the electric bulb is

400 Ohms

.
Given:
Power,

P = 100 W

and potential difference

V = 200 V

It is known that the power is given by the formula

P = V \times I

Where

P

V

and

I

are the power, potential difference and current, respectively.
On substituting the given values, we get current as

\Rightarrow 100 = 200 \times I

\Rightarrow I = 0.5 A

According to Ohm's law, " At a constant temperature, the current in a conductor (

I

) between two terminals is directly proportional to the voltage (

V

) across the points."
Mathematically,

I \propto V

It can also be written as

V = I \times R

Where,

V

is the voltage across the conductor

I =

current flowing through the conductor

R =

resistance provided by the conductor to the flow of the current.
On substituting the given values, we get the resistance as

\Rightarrow 200 = 0.5 \times R

\Rightarrow R = 400 Ω

Hence, the resistance is

400 Ohms

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