Autonomy Session 2: Recap, RC and RL Circuits
Exercise 1
Use voltage division (and other skills) to find the potential drop across R2 in the
following circuits. Write the solutions in terms of variables R1, R2, and R3 before
using their values.
E0=2 V, R1=10 kΩ, R2=10 kΩ, R3=20 kΩ
E0=4 V, R1=20 Ω, R2=10 Ω, R3=25 Ω
Exercise 2
Use current division (and other skills) to find the curent flowing through R2 in the
following circuits. What is the voltage delivered by the current source?
I0=10 A, R1=15 Ω, R2=4 Ω, R3=6 Ω
I0=10 A, R1=15 Ω, R2=10 Ω, R3=5 Ω
Exercise 3 RRC circuit
We consider the circuit represented below, in which a capacitor with
capacitance C and two resistors have resistances R. In the whole problem we
study the voltage drop across the capacitor, u(t).
The switch K is left in position 1 for a
very long time: i.e. the capacitor is
fully charged with potential E.
1) Give expressions for i(∞) and u(∞)
for the permanent regime.
At some time we switch to position 2, and call this time t=0.
2) What is the initial potential across the capacitor u(0)?
3) Establish the differential equation governing u(t).
4) Solve the differential equation and graph the function u(t) for t≥0.
5) Derive an expression for the current i(t), and graph it for t≥0.
Exercise 4
RL circuit with pulse of voltage
We consider an RL circuit in series with a voltage
generator which produces an impulse of voltage e(t)
of value E starting from t=0s until t=1s:
For t < 0, we have i(t)=0
and e(t)=0
We are given L=10 H, R=10 Ω, and E=20 V.
1) Establish the expression for i(t), the current flowing through the circuit, following the
voltage step at t=0 s, and deduce the expression of u(t), the voltage across the inductor.
2) Deduce the expression of the voltage uR(t), the potential drop across the resistor.
3) What is the value of the time constant of the circuit?
4) Calculate the values of i(1s) and u(1s).
We consider now that the time scale begins at t=1s, by defining t’ = t – 1
5) Determine the expressions of i(t’), u(t’), and uR(t’) for t’≥0.
6) Make a figure representing i(t) and a figure representing e(t), u(t), and uR(t) for all t.
Model solution ex 1
Model solution ex 2