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Rates of change and differential equations — Question 18

QCAA 2021, Paper 1 · 6 marks

Q18 · 2021 · Technology-freeComplex unfamiliar6 marks

QUESTION 18 (6 marks)

This differential equation can be used to determine the current II (amperes) at time tt (seconds) with voltage VV (volts) in an electric circuit containing a resistance RR (ohms): kdIdt+RI=V,k\frac{dI}{dt}+RI=V, where kk, RR and VV are positive constants and t≥0t\ge0. Assuming that there is no current in the electric circuit initially, show that the size of the current can never be greater than V/RV/R.
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