Questions and Answers
What is the value of current $I_1$ calculated using mesh analysis?
What is the power dissipation across the $4 ext{Ω}$ resistor?
Which of the following is the correct expression for $I_3$?
What is the total power dissipated in the circuit?
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What is the value of current $I_2$ as determined from the mesh analysis calculations?
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Study Notes
Mesh Analysis for Power Dissipation
- Mesh analysis is utilized to calculate the currents in a circuit with resistors.
- Variables defined:
- ( I_3 = -I_1 ): indicating the relationship between currents in the circuit.
- ( I_3 = 0.5I_0 - 0.5I_1 ): another expression relating current ( I_0 ).
Setting Up Equations
- The first mesh equation:
- ( I_1 + 4(I_1 - I_3) + 56 = 0 ).
- Simplifying the equation:
- ( I_1 + 4I_1 - 4I_3 + 56 = 0 ).
- Upon substituting ( I_3 = -0.5I_1 ):
- ( I_1 + 4I_1 + 2I_1 + 56 = 0 ) leading to ( I_1 = -8A ).
Calculating Other Currents
- From ( I_3 = -0.5I_1 ):
- ( I_3 = 4A ).
- Using the second mesh equation:
- ( -56 + 8(I_2 - I_3) + 2I_2 = 0 ) leads to:
- ( -56 + 8(I_2 - 4) + 2I_2 = 0 ).
- Solving gives ( I_2 = 8.8A ).
Power Dissipation Calculations
-
Resistor at 1Ω:
- Power ( P_{1\Omega} = I_1^2 = 64W ).
-
Resistor at 4Ω:
- Power ( P_{4\Omega} = 4(I_1 - I_3)^2 = 576W ).
-
Resistor at 8Ω:
- Power ( P_{8\Omega} = 8(I_2 - I_3)^2 = 184.32W ).
-
Resistor at 2Ω:
- Power ( P_{2\Omega} = 2I_2^2 = 154.88W ).
Summary of Results
- Calculated currents: ( I_1 = -8A ), ( I_2 = 8.8A ), ( I_3 = 4A ).
- Power dissipated in various resistors spans from ( 64W ) to ( 576W ).
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Description
This quiz focuses on using mesh analysis to calculate the power dissipated in various resistors in a circuit. You'll need to apply equations related to current and power to determine the outcomes for each resistor. Test your understanding of circuit analysis concepts.
