The magnetic flux ϕ (in weber) linked with a closed circuit of resistance 8Ω varies with

Question

The magnetic flux \(\phi\) (in weber) linked with a closed circuit of resistance \(8 \Omega\) varies with time (in seconds) as \(\phi =5t^2 -36t+1.\) The induced current in the circuit at t = 2s is _____ A.

Answer 1

Correct answer is : 2

\(\varepsilon =-\frac {d\phi}{dt}\)

\(=\frac {-d\phi}{dt}(5t^2 - 36 t +1)\)

\(\varepsilon =-[10t -36]\)

Now at t = 2 sec

\(\varepsilon = -[10\times 2-36]\)

\(q =-[20-36]\)

\(\varepsilon =16\)

Now \(i = \frac {\varepsilon}{R}\)

\(i = \frac {16}{8}\)

\(\Rightarrow i = 2A\)