At the moment of 1 and t=0+, the equivalent circuit diagram of the circuit is as follows:
The capacitor voltage cannot change suddenly, so uc(0+)=uc(0-)=9V, so:
Obviously, the voltage across the 6 Ω resistor is now: u (0+) = UC (0+) = 9V; The potentials at both ends of the10Ω resistor are equal, so i(0+)=0A.
2. When t=∞, a fully charged capacitor is equivalent to an open circuit, so I (∞) = 9/(10+6) = 9/16 (a) = 0.5625a..
u(∞)=i(∞)×6=0.5625×6=3.375(V).
3. Find the time constant τ: equivalent resistance r =10 ∨ 6 =15/4 = 3.75 (ω).
Therefore: τ=RC=3.75×2=7.5(s).
4、f(t)=f(∞)+[f(0+)-f(∞)]e^(-t/τ)。
Therefore: I (t) = 0.5625+(0-0.5625) E (-t/7.5) = 0.5625-0.5625 E (-t/7.5) A.
U (t) = 3.375+(9-3.375) E (-t/7.5) = 3.375+5.625 E (-t/7.5) V. 。