Apply Thevenin's theorem to find Vo in the circuit of the figure. Consider R= 5Q. 42 12 ww- ЗА 16Ω R 12 V The value of Vis V. ww
Apply Thevenin's theorem to find Vo in the circuit of the figure. Consider R= 5Q. 42 12 ww- ЗА 16Ω R 12 V The value of Vis V. ww
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Transcribed Image Text:**Title: Applying Thevenin’s Theorem to Find the Output Voltage in a Circuit**
**Objective:**
Use Thevenin’s theorem to determine the output voltage \( V_o \) in the given circuit.
**Circuit Components:**
- A 3 A current source
- A 16 Ω resistor
- A 4 Ω resistor
- A 1 Ω resistor
- A 5 Ω resistor
- A voltage source of 12 V
- Resistor \( R \) with a value of 5 Ω
- Output voltage \( V_o \) across the 1 Ω resistor
**Description:**
The circuit consists of a parallel and series combination of resistors and sources. A 3 A current source is connected in parallel to a 16 Ω resistor. This parallel configuration is connected in series with a 4 Ω resistor and a combination containing two branches. One branch consists of a 5 Ω resistor and a 12 V voltage source. The other branch includes a 1 Ω resistor with an output voltage \( V_o \) across it. The resistor \( R \) is given as 5 Ω, and it is connected in series before the 1 Ω resistor.
**Task:**
Calculate the output voltage \( V_o \) using Thevenin’s theorem, considering \( R = 5 \) Ω.
**Solution:**
1. **Thevenin’s Equivalent Voltage (\( V_{th} \)):**
Find the open-circuit voltage across the 1 Ω resistor by considering the contributions from each source and resistor combination.
2. **Thevenin’s Equivalent Resistance (\( R_{th} \)):**
Determine the equivalent resistance seen from the terminals across the 1 Ω resistor with independent sources turned off (current source open-circuited, voltage source short-circuited).
3. **Calculate \( V_o \):**
Use \( V_{th} \) and \( R_{th} \) with the Thevenin equivalent circuit to find \( V_o \) using Ohm’s Law.
**Conclusion:**
The value of \( V_o \) is determined by analyzing the circuit using Thevenin’s theorem, simplifying the complex circuit to a single voltage source and series resistance to ease the calculation of the voltage across the 1 Ω resistor. Fill in the calculated voltage in the provided space.
\[
\text{The value of } V_o \text{
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