Step response worksheet with answers

Free printable Step response worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

An uncharged capacitor C = 2.2 µF is charged from a 9 V step source through a resistor R = 10 kΩ. Find the 10–90 % rise time t_r of the capacitor voltage, in ms.

R = 10 kΩC = 2.2 µFV = 9 V

t_r = ms

2.Easy

An uncharged capacitor C = 100 µF is charged from a 12 V step source through a resistor R = 47 kΩ. How long after closing the switch does the capacitor voltage reach 50 % of its final value? Find t in ms.

R = 47 kΩC = 100 µFV = 12 V50 %

t = ms

3.Medium

A system has the transfer function G(s) = 42/(s² + 7s + 42) and receives a unit step input. The poles are s = σ ± jω_d. Find the real part σ.

G(s) = 42/(s² + 7s + 42)

σ =

4.Medium

A system has the transfer function G(s) = 267/(s² + 3s + 89) and receives a unit step input. The poles are s = σ ± jω_d. Find the real part σ.

G(s) = 267/(s² + 3s + 89)

σ =

5.Hard

A series RLC circuit with R = 6 Ω, L = 10 mH and C = 100 µF is connected to a 12 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the percent overshoot %OS of the capacitor voltage.

R = 6 ΩL = 10 mHC = 100 µFV = 12 V

%OS = %

6.Hard

A series RLC circuit with R = 300 Ω, L = 500 mH and C = 2 µF is connected to a 12 V step at t = 0. The capacitor is uncharged and no current flows before the step. Find the peak capacitor voltage v_C,max.

R = 300 ΩL = 500 mHC = 2 µFV = 12 V

v_C,max = V

Answer key

1. t_r = 48.34 ms
2. t = 3258 ms
3. σ = −3.5
4. σ = −1.5
5. %OS = 37.23 %
6. v_C,max = 16.47 V

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