If the current through a bulb changes by 1%,w | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The power consumed by a bulb is given by the formula $P = i^2R$,where $i$ is the current and $R$ is the resistance.Since $R$ is constant,we have $

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) The power consumed by a bulb is given by the formula $P = i^2R$,where $i$ is the current and $R$ is the resistance.Since $R$ is constant,we have $P \propto i^2$.Taking the derivative or using the approximation for small changes,we get $\frac{\Delta P}{P} = 2 \frac{\Delta i}{i}$.Given that the percentage change in current is $\frac{\Delta i}{i} 	imes 100 = 1\%$.Therefore,the percentage change in power is $\frac{\Delta P}{P} 	imes 100 = 2 	imes (\frac{\Delta i}{i} 	imes 100) = 2 	imes 1\% = 2\%$.Thus,the power consumed changes by $2\%$.

If the current through a bulb changes by $1\%$,what is the percentage change in the power consumed?

Similar Questions

The energy consumed in a $1\, kW$ electric heater in $30$ seconds will be:

In a building,there are $15$ bulbs of $45 \; W$,$15$ bulbs of $100 \; W$,$15$ small fans of $10 \; W$,and $2$ heaters of $1 \; kW$. The voltage of the electric main is $220 \; V$. The minimum fuse capacity (rated value) of the building will be: .......... $A$

The battery of a mobile phone is rated as $4.2 \ V, 5800 \ mAh$. How much energy is stored in it when fully charged (in $kJ$)?

Assertion : When current through a bulb decreases by $0.5\%$,the glow of bulb decreases by $1\%$.
Reason : Glow (Power) is directly proportional to the square of current.

$A$ heating element is designed to dissipate $2400 \, W$ when connected to $240 \, V$. The power it dissipates when it is connected to $120 \, V$ is (Assume that resistance of the filament is constant). (in $ \, W$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module