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Question 19.SP.6: For the circuit shown (Fig. 19-11), a 40-μF capacitor is add......

For the circuit shown (Fig. 19-11), a 40-μF capacitor is added across the 20-μF capacitor in the circuit of Fig. 19-10. Find the time constant of this circuit and the voltage across this circuit 3 s after the start of charge.

19.11
19.10
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Find the total capacitance for two capacitors in parallel.

Parallel:   CT=C1+C2=20+40=60 μFC_T=C_1+C_2=20+40=60\ \mu F

Then   T=RCT=(100×103)(60×10−6)=6 sT=R C_T=\left(100 \times 10^3\right)\left(60 \times 10^{-6}\right)=6\ s

Write the formula for charging voltage and substitute values to find vCv_{C}.

vC=V(1−e−t/RC)v_C=V\left(1-e^{-t / R C}\right)    (19-17)

=10(1−e−3/6)=10(1−e−0.5)=10(1−0.607)=10(0.393)=3.93 V=10\left(1-e^{-3 / 6}\right)=10\left(1-e^{-0.5}\right)=10(1-0.607)=10(0.393)=3.93\ V

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