Question

A 12.7kΩ resistor and a capacitor are connected in series and then a 12.0 V potential difference is suddenly applied across them. The potential difference across the capacitor rises to 7.54 V in 1.64μs. Calculate the time constant of the circuit.

Answer 1

To calculate the time constant of the RC circuit, use the formula T = -t / ln(1 - V(t)/V_{max}), plugging in the provided values for time, voltage across the capacitor, and the maximum voltage.

Step-by-step explanation:

The question is about calculating the time constant of an RC (resistor-capacitor) circuit. To find the time constant, we use the formula T = RC, where T is the time constant, R is the resistance, and C is the capacitance.

Given that the potential difference across the capacitor rises to 7.54 V in 1.64μs, we can use the formula involving the time constant T, which states that the voltage across a charging capacitor at any time t is V(t) = V_{max}(1 - e^{-t/T}), where V_{max} is the maximum voltage (in this case, 12.0 V).

Here's the equation rearranged to solve for the time constant T: T = -t / ln(1 - V(t)/V_{max}). Substituting the given values (1.64μs for t and 7.54 V for V(t)) and performing the calculation will yield the time constant.