After two time constants, the capacitor in...

Question 1 of 27070hroZDQt5zC1YejdMkdtR

After two time constants, the capacitor in an RC circuit is discharged to what percentage of the starting voltage?

Back

Question 1 of 27070

Q

After two time constants, the capacitor in an RC circuit is discharged to what percentage of the starting voltage?

🔍 Key Concepts

• RC time constant (τ) and the exponential discharge curve V(t) = V₀·e^(−t/τ) • How many time constants have passed when t = 2τ • Converting e^(−2) into a percentage of the initial voltage

💭 Think About

• Write the general formula for capacitor voltage during discharge and substitute t = 2τ. What mathematical expression do you get? • Compare the numerical value of e^(−2) (approximately) to the percentages listed in the choices. • Think about whether the voltage after 2τ should be mostly discharged or mostly remaining. Which range of percentages makes physical sense for a decaying exponential?

✅ Before You Answer

• Be sure you are using the discharge formula, not the charging formula. • Carefully convert the decimal value of e^(−2) into a percentage (multiply by 100). • Confirm that your final percentage matches one of the four options exactly or very closely.