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nadya68 [22]
3 years ago
14

The total charge that has entered a circuit element is q(t) = 6 (1 - e-7t) when t ≥ 0 and q(t) = 0 when t < 0. The current in

the element for t ≥ 0 can be represented as i left-parenthesis t right-parenthesis equals Upper B e Superscript negative a t A where B and a are real constants. Determine the values of B and a.
Mathematics
1 answer:
Bess [88]3 years ago
4 0

Answer:

A=42, B=-7

Step-by-step explanation:

The current function of time is defined as follows:

I(t)=\frac{dq(t)}{dt}

where q(t) is the charge function.

For the given charge function of time q(t)=6\left( 1-e^{-7t}\right) we have the following current function:

I(t)=\frac{d}{dt} \left(6\left( 1-e^{-7t}\right)\right)=42e^{-7t}

In the problem it is proposed that I(t)=Be^{-At}.

Examining the expression of I(t) we obtained by deriving q(t) with the expression proposed by the problem and comparing term by term:

I(t)=Be^{-At}=42e^{-7t}

We conclude that A=-7 and B=42.

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