Openai/691e301d-9ef8-800a-b179-3a4e29e49fe1

This conversation was exported from ChatGPT

gpt-5-1

User: What is the impedance of an 0.1uF capacitor at 50Hz?

What is the impedance of an 0.1uF capacitor at 50Hz?

Assistant: To find the impedance of a capacitor, use:

To find the impedance of a capacitor, use:

ZC=1j 2πfCZ_C = \frac{1}{j \, 2\pi f C}ZC​=j2πfC1​ We usually give the magnitude:

∣ZC∣=12πfC|Z_C| = \frac{1}{2\pi f C}∣ZC​∣=2πfC1​ Given:

• C=0.1 μF=1×10−7 FC = 0.1\,\mu\text{F} = 1\times10^{-7}\,\text{F}C=0.1μF=1×10−7F
• f=50 Hzf = 50\,\text{Hz}f=50Hz

Compute:

∣ZC∣=12π⋅50⋅1×10−7|Z_C| = \frac{1}{2\pi \cdot 50 \cdot 1\times10^{-7}}∣ZC​∣=2π⋅50⋅1×10−71​ ∣ZC∣=13.14159×10−5|Z_C| = \frac{1}{3.14159 \times 10^{-5}}∣ZC​∣=3.14159×10−51​ ∣ZC∣≈31831 Ω|Z_C| \approx 31831\,\Omega∣ZC​∣≈31831Ω So:

Complex form:

ZC≈−j 31.8 kΩZ_C \approx -j\,31.8\,\text{k}\OmegaZC​≈−j31.8kΩ (It's purely reactive and negative imaginary.)