Multiple Choice 10 points What is the expected time constant created when a \( 0.31 \mu \mathrm{~F} \) capacitor is connected in series with a 270 ohm resistor? \( 871 \mu \mathrm{~s} \) \( 841 \mu \mathrm{~s} \) \( 84 \mu \mathrm{~s} \) \( 8.4 \mu \mathrm{~s} \) \( 0.115 \mu \mathrm{~s} \)

To find the time constant \( \tau \) for a resistor-capacitor (RC) circuit, we use the formula: \[ \tau = R \times C \] where \( R \) is the resistance in ohms (Ω) and \( C \) is the capacitance in farads (F). In this case, we have \( R = 270 \, \Omega \) and \( C = 0.31 \, \mu F = 0.31 \times 10^{-6} \, F \). Calculating: \[ \tau = 270 \, \Omega \times 0.31 \times 10^{-6} \, F = 83.7 \times 10^{-6} \, s = 83.7 \, \mu s \] Now rounding this gives us approximately \( 84 \, \mu s \). So the expected time constant created is \( 84 \mu \mathrm{~s} \).