Question
Download Solution PDFA ramp voltage V(t) = 100 V is applied to an RC differentiating circuit with R=5 kΩ and C = 4 μF. The maximum output voltage is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
In an RC differentiating circuit, the output voltage is proportional to the rate of change (derivative) of the input voltage. For a ramp input signal, \( V(t) = at \), the derivative is constant: \( \frac{dV}{dt} = a \).
The output voltage for a differentiating circuit is given by:
\( V_{out} = RC \cdot \frac{dV_{in}}{dt} \)
Given
Ramp input: \( V(t) = 100t \) → so \( \frac{dV}{dt} = 100\ \text{V/s} \)
R = 5 kΩ = 5000 Ω
C = 4 µF = \( 4 \times 10^{-6} \) F
Calculation
Using the formula:
\( V_{out} = RC \cdot \frac{dV_{in}}{dt} \)
\( V_{out} = 5000 \cdot 4 \times 10^{-6} \cdot 100 = 2\ \text{V} \)
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