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Question 542

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

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.

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