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The total charge that has entered circuit element is q(t) = 0.50 (1 – e-5t) when t ≥ 0 and q(t) = 0 when t < 0. Determine the current in this circuit element for t ≥ 0
  • a)
    i(t) = -0.250e-5t A
  • b)
    i(t) = 2.5e-5t A
  • c)
    i(t) = -0.50(1 - e-5t) A
  • d)
    i(t) = -0.50(t + 0.2e-5t) A
Correct answer is option 'B'. Can you explain this answer?
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The total charge that has entered circuit element is q(t) = 0.50 (1 &n...
Given that, q(t) = 0.50 (1 – e-5t)
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The total charge that has entered circuit element is q(t) = 0.50 (1 &n...
Explanation:

Given Charge Function:
- q(t) = 0.50 (1 - e^(-5t)) for t ≥ 0
- q(t) = 0 for t < 0

Current Formula:
- The current (i) in a circuit element is given by the derivative of the charge function with respect to time, i(t) = dq(t)/dt

Derivative of Charge Function:
- Taking the derivative of q(t) with respect to t, we get:
- dq(t)/dt = 0.50 * 5e^(-5t) = 2.5e^(-5t)

Current Calculation:
- Therefore, the current in the circuit element for t ≥ 0 is:
- i(t) = 2.5e^(-5t) A

Conclusion:
- The correct answer is option B: i(t) = 2.5e^(-5t) A, as derived from the given charge function and the formula for current in a circuit element.
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The total charge that has entered circuit element is q(t) = 0.50 (1 – e-5t) when t ≥ 0 and q(t) = 0 when t < 0. Determine the current in this circuit element for t ≥ 0a)i(t) = -0.250e-5tAb)i(t) = 2.5e-5tAc)i(t) = -0.50(1 - e-5t) Ad)i(t) = -0.50(t + 0.2e-5t) ACorrect answer is option 'B'. Can you explain this answer?
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