95.0k views
1 vote
If VC(0) = -450 V, choose the correct expression for Vo for t ≥ 0.

A) Vo(t) = -450e^(0.5t)
B) Vo(t) = -450e^(-0.5t)
C) Vo(t) = -450e^(2t)
D) Vo(t) = -450e^(-2t)

User Zeroliu
by
8.0k points

1 Answer

4 votes

Final answer:

The correct expression for the voltage across a discharging capacitor for time t ≥ 0 with an initial voltage of -450 V is Vo(t) = -450e^(-0.5t). This shows the exponential decay of voltage over time, with the negative exponent indicating a decrease in voltage as time increases. Hence, the correct option in the final answer is B) Vo(t) = -450e^(-0.5t).

Step-by-step explanation:

The student's question involves determining the correct expression for the voltage across a discharging capacitor, Vo, for time t ≥ 0, given the voltage at time zero, VC(0) = -450 V. According to the formula for a discharging capacitor, V equals Vo multiplied by e to the power of negative t divided by RC, where V is the voltage at time t, Vo is the initial voltage, R is the resistance, and C is the capacitance of the circuit.

As no resistance or capacitance values are given, and we assume a standard decay function without any modifications, we look for an option that shows the voltage decreasing exponentially over time. The correct option should therefore be an equation with a negative exponent, indicating that the voltage decreases. From the options given, the correct expression for Vo for t ≥ 0 is Vo(t) = -450e^(-0.5t), where the initial voltage of -450 V decays over time. The negative exponent indicates a conventional discharge curve where the voltage approaches zero as time progresses. Hence, the correct option in the final answer is B) Vo(t) = -450e^(-0.5t).

User Pizzicato
by
8.2k points