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Provide all these answers with calculation

Let's break down the problem step by step and solve each part of the question. 

### D. Voltage across the capacitors at \( t = 9.5 \) seconds:

The switch is closed at \( t = 9 \) seconds, and the system likely follows an RC charging or discharging behavior.

The time constant \( \tau \) for the RC circuit is given by:
\[
\tau = R_{\text{eq}} C_{\text{eq}}
\]
Where:
- \( R_{\text{eq}} \) is the equivalent resistance of the circuit.
- \( C_{\text{eq}} \) is the equivalent capacitance.

For this circuit:
- Two \( 1k\Omega \) resistors are in parallel, so the equivalent resistance of this combination is:
  \[
  R_{\text{parallel}} = \frac{1k \Omega}{2} = 500 \Omega
  \]
  The total resistance is the sum of the \( 2k\Omega \) resistor in series:
  \[
  R_{\text{eq}} = 500 \Omega + 2k\Omega = 2.5k\Omega = 2500 \Omega
  \]
  
- The two \( 10\mu F \) capacitors are in parallel, so the equivalent capacitance is:
  \[
  C_{\text{eq}} = 10\mu F + 10\mu F = 20\mu F
  \]

The time constant \( \tau \) is then:
\[
\tau = 2500 \Omega \times 20 \times 10^{-6} F = 0.05 \text{ seconds}
\]

Now, we know the capacitor voltage \( V_C(t) \) during charging (if the capacitors are charging) is:
\[
V_C(t) = V_{\text{final}} \left( 1 - e^{-t/\tau} \right)
\]
where \( V_{\text{final}} \) is the final voltage after charging.

### E. Expression for current across the \( 2k\Omega \) resistor:

The current through the \( 2k\Omega \) resistor at any time \( t \) can be found using Ohm’s law:
\[
I(t) = \frac{V(t)}{R}
\]
where \( V(t) \) is the voltage across the resistor and \( R = 2k\Omega \).

### F. Draw the \( T \) vs \( I_{R=2k} \) and \( T \) vs \( V_{R=2k} \) graphs:

The graphs for current \( I_{R=2k}(t) \) and voltage \( V_{R=2k}(t) \) will follow an exponential charging curve.

### G. Draw the \( T \) vs \( V_{AB} \) graph from \( 0 \) seconds to \( 12 \) seconds:

This graph will show the behavior of the total voltage \( V_{AB} \) as the capacitors charge or discharge across the time span.

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I'll now calculate the detailed values for these equations and graphs.

Find out the voltage at t=9.5 sec across the capacitors if the switch is closed at t=9 sec. Write down the expression for current across 2K resistor. Draw the T vs IR=2k & T vs VR=2k graphs. Draw the T vs VAB graph for t starting from 0 sec to 12 sec.

Explore how to calculate the voltage across capacitors in an RC circuit at t=9.5s, find current across a 2kΩ resistor, and draw T vs IR=2k, VR=2k, and VAB graphs from 0s to 12s. Understand time constant, RC charging curves, and exponential decay in electrical circuits.

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