In the circuit in the following figure, the resistor is adjusted for critical damping. The initial capacitor voltage is 15 V, and the initial inductor current is 6 mA and R=1250 ohms
Find vC(t) for t≥0.
Express your answer in terms of t, where t is in milliseconds.
The Attempt at a Solution
the only part of this problem i am not getting is solving for the constants with the given initial conditions... the 2 roots to the differential equation are -5000. so:
dv/dt [at t=0+]=-5000*C_1+C_2=i/c=(6*10^-3)A/(320*10^-9 F)=18750 volts/s
so C_2 -5000*15=18750...C_2=93750
but apparently C_2 is actually equal to 56250....If the equation was C_2-5000*15=-18750, then i would get 56250...where am i going wrong???