Question

Which of the following bulbs offers more resistance?
(A) $ 60{\text{ }}W{\text{ }} - {\text{ }}220{\text{ }}V $
(B) $ 100{\text{ }}W{\text{ }} - {\text{ }}250{\text{ }}V $

Answer 1

Hint :This question can be easily solved by using the relationship between power, voltage and resistance of a wire. On substituting all the values in the formula of power one by one those are given in the options we can easily determine the bulb which offers the maximum resistance.
Ohm's law: $ V = I \times R $
power law equation: $ P = I \times V $
where $ V $ stands for voltage, $ I $ for current, $ R $ for resistance, and $ P $ for power
and to determine that which of the bulb offers the maximum resistance we used
 $ R = \dfrac{{{V^2}}}{P} $ .

Complete Step By Step Answer:
Given: two bulbs of rating as (i) $ 60{\text{ }}W{\text{ }} - {\text{ }}220{\text{ }}V $ (ii) $ 100{\text{ }}W{\text{ }} - {\text{ }}250{\text{ }}V $
To determine which of these two bulbs provides the most resistance, use the following formula:
We can deduce the following from Ohm's law: $ V = I \times R $
and by the power law equation: $ P = I \times V $ ,
where $ V $ stands for voltage, $ I $ for current, $ R $ for resistance, and $ P $ for power.
When we divide both equations, we get;
 $ \dfrac{V}{P} = \dfrac{R}{V} $
 $ \Rightarrow R = \dfrac{{{V^2}}}{P} $
Now for first bulb, $ {R_1} = \dfrac{{{{\left( {200} \right)}^2}}}{{60}} = 806.7\Omega $
And for second bulb, $ {R_2} = \dfrac{{{{\left( {250} \right)}^2}}}{{100}} = 625\Omega $
When comparing $ {R_1} $ and $ {R_2} $ , the first bulb, i.e., the $ 60{\text{ }}W{\text{ }} - {\text{ }}220{\text{ }}V $ bulb, provides stronger resistance.
The correct option is: (A) $ 60{\text{ }}W{\text{ }} - {\text{ }}220{\text{ }}V $ .

Note :
Electric current is proportional to voltage and inversely proportional to resistance, according to Ohm's law. However, Ohm's law does not apply to all materials. Because unilateral electrical elements like diodes and transistors only allow current to flow in one way, Ohm's law does not apply to them. Voltage and current will not be constant with respect to time for nonlinear electrical elements with factors like capacitance, resistance, and so on, making Ohm's law difficult to apply.