Question

The voltage across a charged capacitor is given by the equation V(t) = 4e^(-0.4t), where t is in seconds. What is the voltage after 3 seconds (in volts)? 1) 0.785 2) 1.665 3) 2.297 4) 3.374

Answer 1

To calculate the voltage across a capacitor after 3 seconds using the given function V(t) = 4e^(-0.4t), substitute t with 3. The resulting voltage is approximately 1.665 volts.

Step-by-step explanation:

The question asks for the voltage across a charged capacitor at a specific time, given the exponential decay function V(t) = 4e^(-0.4t). To find the voltage after 3 seconds, we simply substitute t with 3 in the equation, resulting in V(3) = 4e^(-0.4*3). By performing this calculation, the voltage comes out to about 1.665 volts, which corresponds to option 2 in the question.

Answer 2

The voltage across the charged capacitor after 3 seconds is approximately 2.297 volts, corresponding to option 3.

Step-by-step explanation:

The given equation for the voltage across a charged capacitor is where

t is the time in seconds. To find the voltage after 3 seconds, substitute

t=3 into the equation:

Therefore, the correct answer is option 3, 2.297 volts.

Understanding the behavior of charging or discharging capacitors involves mathematical models like the exponential function in this case. The parameter 0.4 in the exponent determines the rate of decay, and the time t influences the voltage. In this context, after 3 seconds, the voltage decreases but is still approximately 2.297 volts.

This type of exponential decay is common in electrical circuits involving capacitors. The calculation not only provides the voltage at a specific time point but also offers insights into the transient behavior of the circuit, aiding in the analysis and design of electronic systems.