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1.9.31 Formulate first order differential equations (A-level only)

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Question 10

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]

1.9.31 Formulate first order differential equations (A-level only) Questions

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