What is the time constant of a circuit with a 100-microfarad capacitor and a 470-kilohm resistor in series?

To determine the time constant of a circuit involving a capacitor and a resistor in series, you can use the formula:

[ \tau = R \times C ]

where ( \tau ) is the time constant in seconds, ( R ) is the resistance in ohms, and ( C ) is the capacitance in farads.

In this case, the values given are:

• Resistance ( R = 470 , \text{k}\Omega = 470,000 , \Omega )

• Capacitance ( C = 100 , \mu\text{F} = 100 \times 10^{-6} , \text{F} )

Substituting these values into the formula gives:

[

\tau = 470,000 , \Omega \times 100 \times 10^{-6} , \text{F}

]

[

\tau = 470,000 \times 0.0001 = 47 , \text{seconds}

]

This calculation shows that the time constant is indeed 47 seconds, which corresponds to the chosen answer. The time constant is significant in RC circuits as it defines the time it takes for the charge