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3.6 Integration (A-level only)

3.6 Integration (A-level only)

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Question 168

The current, xxx amps, at time ttt seconds after a switch is closed in an electric circuit is modelled by the differential equation

dxdt=k−2x \frac{dx}{dt} = k - 2x dtdx​=k−2x

where kkk is a constant. Initially, there is no current in the circuit.

a.

Solve the differential equation to show that x=k2(1−e−2t)x = \frac{k}{2}(1 - e^{-2t})x=2k​(1−e−2t).

[4]
b.

In the long term, the current in the circuit approaches 12 amps.

Find the value of kkk.

[2]
c.

Find the time, in seconds, for the current to reach 8 amps, giving your answer to 2 significant figures.

[4]
Markscheme

3.6 Integration (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Integration (A-level only)

363 exam-style questions on CCEA A Level Maths 3.6 Integration (A-level only), covering 3.6.1 Integration (A-level only), 3.6.2 Integration (A-level only), 3.6.3 Integration (A-level only), 3.6.4 Integration (A-level only), 3.6.5 Integration (A-level only), 3.6.6 Integration (A-level only), and 3.6.7 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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