Starting with V = v0 e – t/RC ,
show that C = t1/2 / 0.693 * R
Derive time dependence of voltage and current for a capacitor equation v(t)=V(1-e-t/RC) i(t)=(V/R)(e-t/RC)
Rearrange V(t)/Vo = e^-t/RC to solve for C
Show that C = [T1/2]/[R*ln(2)], where T1/2 is the half-life (time interval required for the voltage/or charge to fall to one-half of its initial value) and RC time constant is τ = R*C.
R V.(t) CE + V.(0) Figure 2. The RC circuit. P1 For the RC circuit given in Figure 2 a) Obtain the transfer function Vols for Vs=Vmcosot. b) Draw the amplitude response and the phase response. c) According to the value of 0/0, as 0, 1, 2, 3, 10, 20, 100 and oo, calculate the H and 6.
1 Show that the discharge of a capacitor obeys the exponential equation q(t) = 2.e-t/RC And that the instantaneous current in the circuit obeys the expression 1 = Q RC e
The switch on an RC circuit is closed at t = 0. Given that E = 9.0 V , R = 180 Ω and C = 24 μF , how much charge is on the capacitor at time t = 4.2 ms ?
• Let V be a 2-dimensional real vector space, and let T E End(V). Show that T is diagonalizable over C but not over R if and only if tr(T)2 < 4. det(T).
rc time constant: At the circuit below detemine the ratio T2/T1 When T1 is the time constant at t=0 when the swith is closed and T2 is the time constant afyer closing the switch. Answer from the book is T2/T1 = 2
Consider an RC circuit with E = 12.0 V ,R = 180 Ω , and C = 45.8 μF . (a) Find the time constant for the circuit. (b) Find the maximum charge on the capacitor. (c) Find the initial current in the circuit.
04 (2) A rectangular pulses, E (t) is applied to the RC circuit as shown in Figure Q4(2). (1) Show that the circuit can be modelled as RC + V = (1) -4(-2) (ii) Calculate the response, or with C) = 0 ning Laplace transform. mark b) Consider the network circuit as shown in Figure Q4 (b) with initial current and their derivatives are zero fort = 0. 1) Show the loop current is can be formulated as dig dt...