Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • The charge flown through a resistance R in time t varies with time according to <img alt="\mathrm{Q}=\mathrm{at}-\mathrm{bt}^2" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7BQ%7D

The charge flown through a resistance R in time t varies with time according to \mathrm{Q}=\mathrm{at}-\mathrm{bt}^2.
 The total heat produced in R by the time current becomes zero is :

Option: 1

\frac{a^3 R}{6 b}


Option: 2

\frac{a^3 R}{2 b}


Option: 3

\frac{a^3 R}{3 b}


Option: 4

\frac{a^3 R}{b}


Answers (1)

best_answer

\mathrm{Q}=\mathrm{at}-\mathrm{bt^{2 }}           \Rightarrow       \mathrm{i}=\frac{\mathrm{dQ}}{\mathrm{dt}}=\mathrm{a}-2 \mathrm{bt}

Current becomes zero at time   t=\frac{a}{2 b}

Total heat produced  =\int_{t-0}^{t-2 / 2 b} i^2 R d t=\int_0^{a / 2 b}(a-2 b t)^2 R d t=\frac{a^3 R}{6 b}

Posted by

Rishi

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2026: NIT Rourkela records higher closing ranks in CSE, ECE, AI; core engineering branches stable
anam-khan

JEE Main 2026: IIT Delhi’s CSE, EE most opted; last 2 year’s closing ranks for all categories
anam-khan

Must provide CBSE 11th registration numbers to JEE Mains aspirants, board tells schools

Latest Question