What is the time constant of a series circuit where the capacitor is 0.330μf and the resistor is 10ω ?

Explanation:

Take at look to the picture I attached you, using Kirchhoff's current law we get:

This is a separable first order differential equation, let's solve it step by step:

Express the equation this way:

integrate both sides, the left side will be integrated from an initial voltage v to a final voltage V, and the right side from an initial time 0 to a final time t:

Evaluating the integrals:

natural logarithm to both sides in order to isolate V:

Where the term RC is called time constant and is given by:

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