What is the voltage across a capacitor (V) after one time constant in an RC char
Practice Questions
Q1
What is the voltage across a capacitor (V) after one time constant in an RC charging circuit?
V = V0(1 - e^(-t/τ))
V = V0 * e^(-t/τ)
V = V0(1 + e^(-t/τ))
V = V0 * t/τ
Questions & Step-by-Step Solutions
What is the voltage across a capacitor (V) after one time constant in an RC charging circuit?
Step 1: Understand the components of the formula. V0 is the maximum voltage the capacitor can reach, e is a mathematical constant (approximately 2.718), t is the time in seconds, and τ (tau) is the time constant of the circuit.
Step 2: Know that one time constant (τ) is the time it takes for the capacitor to charge to about 63.2% of its maximum voltage (V0).
Step 3: Substitute t with τ in the formula V = V0(1 - e^(-t/τ)). This gives you V = V0(1 - e^(-1)).
Step 4: Calculate e^(-1), which is approximately 0.3679.
Step 5: Now, calculate 1 - e^(-1), which is approximately 1 - 0.3679 = 0.6321.
Step 6: Multiply this result by V0 to find the voltage across the capacitor after one time constant: V = V0 * 0.6321.
