Question

If q = t² +4t+ 5, find the instantaneous current at t= 3 seconds and average current from 0 to 2 seconds

Answer 1

Instantaneous current at t= 3 seconds   = 10A , Average current  from 0 to 2 seconds  = 6A   if q = t² +4t+ 5

Explanation:

I  = dq/dt

q =  t² +4t+ 5

=> I  = d( t² +4t+ 5)/dt

=> I =  2t  + 4  

at  t = 3

I  =  2(3) + 4  =  10  A

dq  =  I dt

dq =  (2t + 4)dt

integrating both sides

Δq  =  $\int\limits^2_0 {I} \, dt$

=> Δq  =  $\int\limits^2_0$  (2t  + 4)dt

=> Δq  =    t² +4t ]²₀

=> Δq =  (2² + 4(2))  - 0    = 12

Δt  = 2 - 0  = 2

Average current = Δq/ Δt    = 12/2  =  6   A

instantaneous current at t= 3 seconds   = 10A

Average current  from 0 to 2 seconds  = 6A

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Answer 2

Answer:

Given,

I=3t

2 +2t+5

Time interval t=0 and t=2s

We know that,

I=dtdq

So, the change ∫dq=∫ 02 Idtq=∫ 02

(3t 2 +2t+5)dt=[t 3+t 2 +5t] 02 =(8+4+10)=22C