Question

For the given equation of charge Q=3t²+6t, where Q is in coulombs and t is time in seconds, the initial value of current is:

• A. 0 A
• B. 2 A
• C. 6 A
• D. 9 A

Answer 1

The Correct Option is C

The equation for charge is:

\[ Q(t) = 3t^2 + 6t \]

where:

• \( Q \) is in coulombs (C)
• \( t \) is time in seconds (s)

The initial value of current.

Current (\( I \)) is defined as the rate of change of charge with respect to time:

\[ I(t) = \frac{dQ}{dt} \]

Differentiating the given charge equation:

\[ \frac{dQ}{dt} = \frac{d}{dt}(3t^2 + 6t) \]

\[ I(t) = 6t + 6 \]

The initial current is the current at time \( t = 0 \):

\[ I(0) = 6(0) + 6 = 6 \text{ A} \]

The initial value of current is \(\boxed{6 \text{ A}}\).

Answer 2

\(\text{ The current is the time derivative of charge:}\)
\(I = \frac{dQ}{dt} = 6t + 6\)
\(\text{At } t = 0, \text{ the initial value of current is:}\)
\(I(0) = 6(0) + 6 = 6 \, \text{A}\)
\(\text{Thus, the initial current is 6 A.}\)