In the circuit of the figure & = 3.80 kV, C = 6.50 μF, R₁ = R2 = R3 = 1.03 MQ. With C completely uncharged, switch S is suddenly closed (at t = 0). At t = 0, what are (a) current i₁ in resistor 1, (b) current i2 in resistor 2, and (c) current i3 in resistor 3? At t = ∞ (that is, after many time constants), what are (d)i₁, (e)i2, and (f)i3? What is the potential difference V₂ across resistor 2 at (g)t = 0 and (h)t = Do? R₁ R₂

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### Circuit Analysis Problem

In the circuit of the figure, the following parameters are given:

- Electromotive force (ℰ) = 3.80 kV
- Capacitance (C) = 6.50 µF
- Resistor 1 (R₁) = Resistor 2 (R₂) = Resistor 3 (R₃) = 1.03 MΩ

The circuit initially has the capacitor, C, completely uncharged. At time \( t = 0 \), switch S is suddenly closed.

Determine the following:

1. At \( t = 0 \):
   - \( (a) \) Current \( i_1 \) in resistor 1
   - \( (b) \) Current \( i_2 \) in resistor 2
   - \( (c) \) Current \( i_3 \) in resistor 3

2. At \( t = \infty \) (that is, after many time constants):
   - \( (d) \) \( i_1 \)
   - \( (e) \) \( i_2 \)
   - \( (f) \) \( i_3 \)

3. The potential difference \( V_2 \) across resistor 2:
   - \( (g) \) at \( t = 0 \)
   - \( (h) \) at \( t = \infty \)

#### Circuit Diagram Explanation

The circuit diagram is as follows:

- The battery with electromotive force ℰ is connected in series with resistor \( R_1 \) and switch S.
- Resistor \( R_2 \) is in series with resistor \( R_3 \) and the capacitor C.
- The switch S is initially open, and closing it connects the circuit, allowing current to flow through the resistors and the capacitor.

This setup will involve calculations of initial currents and potential differences as the capacitor begins charging and eventually reaches a steady state after a long time (at \( t = \infty \)).
Transcribed Image Text:### Circuit Analysis Problem In the circuit of the figure, the following parameters are given: - Electromotive force (ℰ) = 3.80 kV - Capacitance (C) = 6.50 µF - Resistor 1 (R₁) = Resistor 2 (R₂) = Resistor 3 (R₃) = 1.03 MΩ The circuit initially has the capacitor, C, completely uncharged. At time \( t = 0 \), switch S is suddenly closed. Determine the following: 1. At \( t = 0 \): - \( (a) \) Current \( i_1 \) in resistor 1 - \( (b) \) Current \( i_2 \) in resistor 2 - \( (c) \) Current \( i_3 \) in resistor 3 2. At \( t = \infty \) (that is, after many time constants): - \( (d) \) \( i_1 \) - \( (e) \) \( i_2 \) - \( (f) \) \( i_3 \) 3. The potential difference \( V_2 \) across resistor 2: - \( (g) \) at \( t = 0 \) - \( (h) \) at \( t = \infty \) #### Circuit Diagram Explanation The circuit diagram is as follows: - The battery with electromotive force ℰ is connected in series with resistor \( R_1 \) and switch S. - Resistor \( R_2 \) is in series with resistor \( R_3 \) and the capacitor C. - The switch S is initially open, and closing it connects the circuit, allowing current to flow through the resistors and the capacitor. This setup will involve calculations of initial currents and potential differences as the capacitor begins charging and eventually reaches a steady state after a long time (at \( t = \infty \)).
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