Final answer:
To find the resistance in the circuit, you can use the formula for the RC time constant and solve for R. Given that the time constant is 0.632 of its full voltage, you can set up an equation and calculate the resistance value to be approximately 25.3 Ω.
Step-by-step explanation:
To find the value of the resistance in the circuit, we can use the formula for the RC time constant. The time constant (τ) is the product of the resistance (R) and capacitance (C). In this case, the time constant is given as 0.632 of its full voltage, which means it reaches 63.2% of its final voltage. We can use this value to find the resistance.
- First, we need to find the time constant τ. We can use the formula τ = R x C.
- Given that the time constant is 0.632, we can set up the equation 0.632 = R x C.
- Plugging in the given values, we have 0.632 = R x 25.0 x 10^-9.
- Solving for R, we find R = 0.632 / (25.0 x 10^-9).
- Calculating the resistance, we get R ≈ 25.3 Ω.