The solution to in Fundamentals of Electric Circuits (Alexander & Sadiku) involves finding the current
Substitute the values into the general step response formula:
Where:
Capacitor voltage cannot change instantly: [ v_C(0^+) = v_C(0^-) = 10.91 , \textV ]
Vi(s) = R1IL(s) + L1(sIL(s) - iL(0))
i(t)=4+2e-10t A, for t>0bold i open paren bold t close paren equals 4 plus 2 bold e raised to the negative 10 bold t power A, for bold t is greater than 0
The circuit consists of a voltage source vi(t), a resistor R1 = 1 Ω, an inductor L1 = 1 H, a capacitor C1 = 0.5 F, and a resistor R2 = 1 Ω. practice problem 7.12 fundamentals of electric circuits
Using voltage divider: [ v_C(0^-) = V_s \times \fracR_2R_1 + R_2 ] [ v_C(0^-) = 12 \times \frac100 , \textk\Omega10 , \textk\Omega + 100 , \textk\Omega ] [ v_C(0^-) = 12 \times \frac100110 = 10.91 , \textV ]
