Math Problem Statement
Solution
To solve for the maximum power transferred in the given circuit, we will follow these steps:
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Determine the Thevenin Equivalent Circuit: We need to find the Thevenin equivalent voltage () and Thevenin equivalent resistance () as seen from the load (the 17-ohm resistor in this case).
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Apply the Maximum Power Transfer Theorem: Maximum power is transferred to the load when the load resistance equals the Thevenin equivalent resistance, i.e., .
Step 1: Calculate Thevenin Equivalent Resistance ()
To find , remove the load (the 17-ohm resistor) and calculate the resistance seen from the open terminals.
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The resistors in series:
Now, this combination is in parallel with the 8-ohm resistor:
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Adding the 22-ohm resistor in series:
Step 2: Calculate Thevenin Voltage ()
We will calculate , the open-circuit voltage across the 17-ohm resistor. This involves voltage division across the resistors in the circuit.
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The total resistance in the loop is:
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The current through the circuit due to the 20V source is:
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The voltage across the 22-ohm resistor (which is in series with the load) can be found using:
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The voltage across the parallel combination of the 5-ohm and 8-ohm resistors is:
Step 3: Maximum Power Transfer
According to the maximum power transfer theorem, the maximum power is transferred to the load when:
The maximum power transferred is given by:
So, the maximum power transferred is approximately 0.153 W.
Would you like more details on any step or have further questions?
Here are 5 related questions for deeper understanding:
- How is the Thevenin resistance calculated in complex circuits?
- What is the significance of the maximum power transfer theorem?
- How can we calculate Thevenin voltage in different configurations?
- What happens if the load resistance is not equal to the Thevenin resistance?
- How does current division differ from voltage division in circuit analysis?
Tip: When analyzing circuits, always double-check if resistors are in series or parallel to avoid calculation errors.
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Math Problem Analysis
Mathematical Concepts
Thevenin's Theorem
Maximum Power Transfer
Circuit Analysis
Formulas
R_th = (R_series || R_parallel)
V_th = V_source - V_drop
P_max = V_th^2 / (4 * R_th)
Theorems
Thevenin's Theorem
Maximum Power Transfer Theorem
Suitable Grade Level
College-level Electrical Engineering or Physics
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