To solve the problems based on the provided circuit diagram, we need to break down each part of the question. Here's a step-by-step analysis for parts D through G.

Part D: Voltage across capacitors at $t = 9.5$ sec

• Before $t = 8$ sec: The capacitors were connected to a different circuit. We assume that they were charged to some voltage. Once they are disconnected and the new circuit is connected at $t = 9$ sec, we need to find the voltage across the capacitors at $t = 9.5$ sec.
• Capacitance: The two $10 \mu F$ capacitors are in parallel, giving an effective capacitance $C_{\text{total}} = 20 \mu F$.
• Discharging Behavior: When the switch closes at $t = 9$ sec, the capacitors will start discharging through the resistors.

We assume the discharge will follow an exponential decay: $V(t) = V_0 \cdot e^{-\frac{t}{RC}}$ where:

• $V_0$ is the initial voltage across the capacitors (just before $t = 9$ sec),
• $R$ is the total resistance the capacitors are discharging through,
• $C$ is the total capacitance,
• $t$ is the time after the switch is closed.

To calculate this fully, we would need more information about the initial conditions or the configuration before $t = 8$ sec. Otherwise, we'd proceed by calculating assuming a typical setup.

Part E: Current across the 2kΩ resistor

For the current through the 2kΩ resistor after the switch closes at $t = 9$ sec, we use Ohm's Law: $I_{R_2} = \frac{V_{R_2}}{R_{2}} = \frac{V(t)}{2000}$ where $V(t)$ is the voltage across the 2kΩ resistor, which depends on the charge remaining in the capacitors as they discharge.

Part F: Graph of $T$ vs $I_{R=2k}$ and $T$ vs $V_{R=2k}$

These graphs will follow an exponential decay since the current and voltage in an RC discharging circuit follow this behavior:

• $I(t)$ and $V(t)$ both decay exponentially with time, as described in Part E.

The general form of the voltage and current will be: $V(t) = V_0 e^{-\frac{t}{RC}} \quad \text{and} \quad I(t) = I_0 e^{-\frac{t}{RC}}$

Part G: $T$ vs $V_{AB}$ graph

This graph will also be similar to the voltage and current curves in an RC discharging circuit, with the voltage across the capacitors decreasing over time according to an exponential function.

To fully solve these problems and draw the graphs, I can help compute numerical values if more information (such as initial voltage) is provided. Would you like to proceed with some assumptions for the missing data, or provide additional details for further calculation?

Follow-up Questions:

1. What was the initial charge on the capacitors before they were disconnected at $t = 8$ seconds?
2. Should we assume that the capacitors were fully charged before being connected to the new