After two time constants, the capacitor in...

Question 1 / 27070DwunYaJ7YMhq6WIez0bQ

Question 1 of 27070DwunYaJ7YMhq6WIez0bQ

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

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Question 1 of 27070

Q

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

🔍 Key Concepts

• Time constant (τ) in an RC charging circuit • Exponential charging equation for a capacitor: Vc = Vs(1 − e^(−t/τ)) • Relationship between multiples of τ (1τ, 2τ, 3τ, etc.) and the percentage of final voltage reached

💭 Think About

• Write the standard formula for capacitor voltage during charging and substitute t = 2τ into it. What expression do you get? • Evaluate the exponential term e^(−2). Approximately what decimal value do you obtain, and what percentage of the supply voltage does that correspond to? • Compare your calculated percentage with the choices given. Which one is closest to your computed result?

✅ Before You Answer

• Be sure you are using the charging formula (1 − e^(−t/τ)), not the discharging one (e^(−t/τ)). • Confirm that you correctly convert the decimal result to a percentage (multiply by 100). • Double-check the approximate value of e^(−2) before matching it to the answer choices.

Question 1 of 27070

Q

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

A

36.8 %

B

63.2 %

C

86 . 5 %

D

95 %

Question 1 / 27070DwunYaJ7YMhq6WIez0bQ

Question 1 of 27070DwunYaJ7YMhq6WIez0bQ

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

Back

Question 1 of 27070

Q

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

🔍 Key Concepts

• Time constant (τ) in an RC charging circuit • Exponential charging equation for a capacitor: Vc = Vs(1 − e^(−t/τ)) • Relationship between multiples of τ (1τ, 2τ, 3τ, etc.) and the percentage of final voltage reached

💭 Think About

• Write the standard formula for capacitor voltage during charging and substitute t = 2τ into it. What expression do you get? • Evaluate the exponential term e^(−2). Approximately what decimal value do you obtain, and what percentage of the supply voltage does that correspond to? • Compare your calculated percentage with the choices given. Which one is closest to your computed result?

✅ Before You Answer

• Be sure you are using the charging formula (1 − e^(−t/τ)), not the discharging one (e^(−t/τ)). • Confirm that you correctly convert the decimal result to a percentage (multiply by 100). • Double-check the approximate value of e^(−2) before matching it to the answer choices.