Physics Problems & Solutions: Electromagnetism

Which two of the following circuits are high-pass filters

A. I and II
B. I and III
C. I and IV
D. II and III
E. II and IV

(GR0177 #39)

Solution:

High-pass filter: V_out ≈ V_in for frequency, ω → ∞

Inductive reactance, X_L = ωL
Capacitive reactance, X_C = 1 / ωC

For ω → ∞
X_L → ∞
X_C → 0

Voltage divider:
$V_{\text{out}}=\left( \frac{R_2}{R_1+R_2}\right ) V_{\text{in}}$

Case I.
$V_{\text{out}}=\left( \frac{R}{R+X_L}\right) V_{\text{in}}=\left( \frac{R}{R+\infty}\right ) V_{\text{in}}=0$
→ Low-pass filter

Case II.
$V_{\text{out}}=\left( \frac{X_L}{R+X_L}\right) V_{\text{in}}=\left( \frac{\infty}{R+\infty}\right ) V_{\text{in}}=V_{\text{in}}$
Note: R ≪ ∞
→ High-pass filter

Case III.
$V_{\text{out}}=\left( \frac{R}{R+X_C}\right) V_{\text{in}}=\left( \frac{R}{R+0}\right ) V_{\text{in}}=V_{\text{in}}$
→ High-pass filter

Case IV.
$V_{\text{out}}=\left( \frac{X_C}{R+X_C}\right) V_{\text{in}}=\left( \frac{0}{R+0}\right ) V_{\text{in}}=0$
→ Low-pass filter

Answer: D

Physics Problems & Solutions

Electromagnetism - High-Pass Filters

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