Determine Resistances in the Circuit

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In summary, to solve the problem of determining the branch currents for maximum power transfer in a circuit driven by a current source, one must replace groups of resistors with a single value and use the rules for resistance in series and parallel. Then, convert the current source to a voltage source using Thevenin's Theorem and choose the appropriate R1 to match the source resistance for maximum power transfer.
  • #1
Kobayashi
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A current is driven from a current source as shown attached. Determine the branch currents if the circuit is configured for maximum power transfer.

Does anyone know how to solve this problem. Any help will be greatly appreciated. Thanks
 

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  • #2
YOu just have to replace groups of resistors with a single value.
Do you know the rules for resitance in series and parallel ?

Work out the combined resistance of the three in parallel ( 16 60 240 ) and draw them as a single resistor 'A'.
Then work out the resistance of 'A' and R1 in series - redraw that as a single resistor 'B'
The you just have the other R16 and B in parallel, work out the resistance of this and then use V = I R
 
  • #3
Okay, I got the combined resistance of the three in parallel, 12V. How do you continue if you don't know R1. Thanks for your help.
 
  • #4
Kobayashi said:
Okay, I got the combined resistance of the three in parallel, 12V. How do you continue if you don't know R1. Thanks for your help.

I take it that you mean the 3 resistors in parallel amount to 12 Ohms.

Do you understand the maximum power transfer theorem? It says for max power transfer to occur, the load resistance must match that of the source. Use Thevenin's Theorem to convert the current source to a voltage source. Then you have to choose R1 to match the source resistance.
 

FAQ: Determine Resistances in the Circuit

How do you calculate the total resistance in a circuit?

In a series circuit, the total resistance is equal to the sum of all individual resistances. In a parallel circuit, the total resistance can be calculated using the formula 1/RT = 1/R1 + 1/R2 + 1/R3 + ... , where RT is the total resistance and R1, R2, R3, etc. are the individual resistances.

What is the unit of resistance?

The unit of resistance is ohms (Ω), named after the German physicist Georg Ohm.

How does temperature affect resistance?

In general, as the temperature increases, the resistance of a material also increases. This is due to the fact that at higher temperatures, the atoms in the material vibrate more, causing more collisions with the electrons and increasing resistance. However, some materials, such as semiconductors, may have a decrease in resistance with an increase in temperature.

How does the length and thickness of a wire affect resistance?

The longer the wire, the higher the resistance, as there is more material for the electrons to travel through. Similarly, the thinner the wire, the higher the resistance, as there is less space for the electrons to flow. This relationship is described by Ohm's Law, which states that resistance is directly proportional to length and inversely proportional to cross-sectional area.

What is the difference between series and parallel circuits in terms of resistance?

In a series circuit, the resistances add up to create a larger total resistance. In a parallel circuit, the total resistance is less than the smallest individual resistance, as the current can split into multiple paths. Additionally, the total resistance in a parallel circuit will always be less than any individual resistance in the circuit.

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