Question

Charge is given as q= (3t^2 +2t +6 ) then find current at 2 sec ?

Answer 1

Answer :

• Current at the instant of 2 s, I = 14 A.

Explanation :

Given :

• Charge ,q = 3t² + 2t + 6
• Instant of time, t = 2 s

To find :

• Current at the instant of 2 s, I = ?

Knowledge required :

• Differentiating the charge with respect to time gives the current.

Current is the change in charge with time.

So,

Formula for current will be :-

⠀⠀⠀⠀⠀⠀⠀⠀⠀I = d(q)/dt⠀

• Power rule of differentiation :

⠀⠀⠀⠀⠀⠀⠀⠀⠀d(x^n)/dx = nx^(n - 1)⠀

• Derivative of a constant term is zero.

⠀⠀⠀⠀⠀⠀⠀⠀⠀d(c)/dt = 0

Solution :

By using the formula for current at a instant and differentiating it with respect to time, we get :

⠀⠀=> I = d(q)/dt

⠀⠀=> I = d(q)/dt = d(3t² + 2t + 6)/dt

⠀⠀=> I = d(q)/dt = d(3t²)/dt + d(2t)/dt + d(6)/dt

⠀⠀=> I = d(q)/dt = [2 × 3t⁽² ⁻ ¹⁾] + [1 × 2t⁽¹ ⁻ ¹⁾] + 0

⠀⠀=> I = d(q)/dt = [2 × 3t1] + [1 × 2t⁰]

⠀⠀=> I = d(q)/dt = 6t + 2

⠀⠀⠀⠀∴ I = 6t + 2 A

Hence the current is 6t + 2 A.

Now finding the current at the instant of 2 s.

By Substituting the value of t in the current, we get :

⠀⠀=> I = 6t + 2 A

⠀⠀=> I₍ₜ ₌ ₂ ₛ₎ = 6(2) + 2

⠀⠀=> I₍ₜ ₌ ₂ ₛ₎ = 12 + 2

⠀⠀=> I₍ₜ ₌ ₂ ₛ₎ = 14

⠀⠀⠀⠀∴ I = 14 A

Hence the current at the instant of 2 s, I = 14 A.

Answer 2

$\large{\boxed{\underline{\sf{Question \: is \: given}}}}$

Charge is given as qv= (3t² + 2t + 6) then find current at 2 seconds ?

$\large{\boxed{\underline{\sf{Answer \: is \: given}}}}$

$\large{\boxed{\underbrace{\sf{Given \: that}}}}$

✠ Given charge = 3t² + 2t + 6

✠ Time = 2 seconds

$\large{\boxed{\underbrace{\sf{To \: find}}}}$

✠ Current at 2 seconds.

$\large{\boxed{\underbrace{\sf{Solution}}}}$

✠ Current at 2 seconds = 14A

$\large{\boxed{\boxed{\sf{Understanding \: the \: question}}}}$

✠ This question says that the charge is given as 3t² + 2t + 6. Afterwards, it ask us to find the current at 2 seconds. The current is produced when there is a differentiating in charge with respect to the time.

$\large{\boxed{\boxed{\sf{Using \: concepts}}}}$

✠ Formula of current.

$\large{\boxed{\boxed{\sf{Using \: formula}}}}$

✠ Formula of current → I = d(q) / dt

$\large{\boxed{\boxed{\sf{More \: Knowledge}}}}$

✠ Power formula of differention ➝ d(xⁿ) / dx = nx(ⁿ - ¹)

✠ Derivatives of constant term 0 ➝ d(c) / dt = 0

$\large{\boxed{\boxed{\sf{Procedure \: of \: the \: question}}}}$

✠ To solve this question we have to use the formula to find the current. Putting the values we get the current as 6t+2. Don't forget to put the symbol A {Ampere} hence, 6t+2A. Now, seeming in 2 seconds as say in question we have to put the values and we get our final result as 14A.

$\large{\boxed{\underbrace{\sf{Full \: solution}}}}$

_________________________________

I = d(q) / dt

• d(3t² + 2t + 6) / dt

• d =(3t²)/ dt + d(2t)/dt +d(6)/dt

• [2×3t(² - ¹) + [1 × 2t(¹ - ¹) + 0

• [2×3t¹] + [1×2t⁰]

• 6t + 2

Therefore, 6t + 2 A is the current.

_________________________________

Now finding current at 2 seconds.

• l = 6t + 2

• l =6(2) + 2

• l = 12 + 2

• l = 14 A

_________________________________