Question - Calculating Thevenin Equivalent Voltage and Resistance
Solution:
To solve for the Thevenin equivalent voltage (V_th) and Thevenin equivalent resistance (R_th) for the given circuit, we will follow these steps:1. Remove the load from the original circuit to isolate the part that will be represented by the Thevenin equivalent. In this case, the "LOAD" is the part we exclude to determine V_th and R_th.2. Calculate the Thevenin voltage (V_th), which is the open-circuit voltage at the terminals where the load was connected. Since there is no current flowing through the 4 Ω resistor (because it is in series with the load and the load is removed), the voltage across the 4 Ω resistor is 0 V. Thus, the Thevenin voltage V_th is the same as the voltage of the voltage source, which is -10 V.3. Calculate the Thevenin resistance (R_th) from the perspective of the load terminals with all independent voltage sources replaced by a short circuit. In this circuit, replacing the voltage source with a short circuit makes the 8 Ω and 4 Ω resistors in parallel. Their combined resistance, R_th, can be calculated using the formula for parallel resistors:$$\frac{1}{R_{th}} = \frac{1}{R_1} + \frac{1}{R_2}$$$$\frac{1}{R_{th}} = \frac{1}{8 \Omega} + \frac{1}{4 \Omega}$$$$\frac{1}{R_{th}} = \frac{1 + 2}{8 \Omega}$$$$\frac{1}{R_{th}} = \frac{3}{8 \Omega}$$$$R_{th} = \frac{8}{3} \Omega$$So, the Thevenin equivalent resistance is $$\frac{8}{3} \Omega$$ or approximately $$2.67 \Omega$$.To summarize:Thevenin voltage (V_th) = -10 VThevenin resistance (R_th) ≈ 2.67 Ω
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