Question

In one experiment, you measured the potential difference across a resistor as a capacitor discharged through it. You then plotted the natural logarithm of the voltage vs time (in seconds), and from the equation of the best fit line you measured the time constant of the RC circuit. If the equation of that line is ln open vertical bar V close vertical bar equals negative 0.027 t plus 2.5 , what is the time constant of the circuit?

Answer 1

Step-by-step explanation:

For discharge of capacitor in RC circuit , the relation is as follows

`V=V_0e^(-t)/(\lambda)`

V is voltage across the capacitor , V₀ is maximum voltage across capacitor , λ is time constant and t is the time after which the voltage is recorded. During discharge this will also be voltage across resistance .

Taking log on both sides

lnV = lnV₀ -
`(t)/(\lambda)`

Given equation

[lnV] = - .027 t + 2.5

Comparing these equation

`(1)/(\lambda) = .027`

λ = 37 s

time constant = 37 sec.