A bulb of \(300 \mathrm{~W}\) and \(220 \mathrm{~V}\) is connected with a source of \(110 \mathrm{~V}\). What is the \(\%\) decrease in power? (A) \(100 . \%\) (B) \(75 \%\) (C) \(70 \%\) (D) \(25 \%\)

Short Answer

Expert verified
The \% decrease in power is \(75\%\).

Step by step solution

01

Calculate the original resistance of the bulb

To find the resistance of the bulb, we will use the formula P = V^2/R, where P stands for Power, V for Voltage, and R for Resistance. Rearranging the formula for R, we have: R = V^2/P Now, plug in the given values of power and voltage: R = (220 \mathrm{~V})^2 / (300 \mathrm{~W}) Calculate the original resistance R: R = 48400 \mathrm{~V^2} / 300 \mathrm{~W} = 161.33 \Omega
02

Calculate the new power when connected to the 110 V source

Now, recalculate the power using the new source voltage (110 V) and the original resistance obtained in step 1. We will reuse the formula P = V^2/R: P_new = (110 \mathrm{~V})^2 / (161.33\Omega) Calculate the new power P_new: P_new = 12100 \mathrm{~V^2} / 161.33 \Omega = 75 \mathrm{~W}
03

Determine the percentage decrease in power

Now, we will calculate the percent decrease in power using the formula: PercentDecrease = [(P_original - P_new) / P_original] * 100 Plug in the values for the original power (300 W) and the new power (75 W): PercentDecrease = [(300 \mathrm{~W} - 75 \mathrm{~W}) / 300 \mathrm{~W}] * 100 Calculate the percentage decrease: PercentDecrease = [225 / 300] * 100 = 0.75 * 100 = 75\% Finally, we compare our result to the given options: PercentDecrease = 75\% The correct answer is (B) 75%.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

There are n resistors having equal value of resistance \(\mathrm{r}\). First they are connected in such a way that the possible minimum value of resistance is obtained. Then they are connected in such a way that possible maximum value of resistance is obtained the ratio of minimum and maximum values of resistances obtained in these way is.... (A) \((1 / n)\) (B) \(\mathrm{n}\) (C) \(\mathrm{n}^{2}\) (D) \(\left(1 / \mathrm{n}^{2}\right)\)

The resistance of a copper coil is \(4.64 \Omega\) at \(40^{\circ} \mathrm{C}\) and \(5.6 \Omega\) at \(100^{\circ} \mathrm{C}\) Its resistance at $0^{\circ} \mathrm{C}$ will be (A) \(5 \Omega\) (B) \(4 \Omega\) (C) \(3 \Omega\) (D) \(2 \Omega\)

Assertion and reason are given in following questions each question has four options one of them is correct select it. (a) Both assertion and reason are true and the reason is correct reclamation of the assertion. (b) Both assertion and reason are true, but reason is not correct explanation of the assertion. (c) Assertion is true, but the reason is false. (d) Both, assertion and reason are false. Assertion: A series combination of cells is used when their internal resistance is much smaller than the external resistance. Reason: It follows from the relation \(\mathrm{I}=\\{(\mathrm{nE}) /(\mathrm{R}+\mathrm{nr})\\}\) Where the symbols have their standard meaning. (A) a (B) \(\mathrm{b}\) (C) \(c\) (D) \(\mathrm{d}\)

The resistance of the wire made of silver at \(27^{\circ} \mathrm{C}\) temperature is equal to \(2.1 \Omega\) while at \(100^{\circ} \mathrm{C}\) it is \(2.7 \Omega\) calculate the temperature coefficient of the resistivity of silver. Take the reference temperature equal to \(20^{\circ} \mathrm{C}\) (A) \(4.02 \times 10^{-3}{ }^{\circ} \mathrm{C}^{-1}\) (B) \(0.402 \times 10^{-3}{ }^{\circ} \mathrm{C}^{-1}\) (C) \(40.2 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}\) (D) \(4.02 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}\)

Assertion and reason are given in following questions each question has four options one of them is correct select it. (a) Both assertion and reason are true and the reason is correct reclamation of the assertion. (b) Both assertion and reason are true, but reason is not correct explanation of the assertion. (c) Assertion is true, but the reason is false. (d) Both, assertion and reason are false. Assertion: There is no current in the metals in the absence of electric field. Reason: Motion of free electrons is random. (A) a (B) \(b\) (C) \(\mathrm{c}\) (D) \(\mathrm{d}\)

See all solutions

Recommended explanations on English Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free