Circuit with Series and parallel resistors, voltage division rule

In summary, the power absorbed by the 15 ohm resistor is 15 W and the goal is to find R. Using the parallel circuit equation and the voltage division rule, R is determined to be 4 ohms when the circuit is simplified and analyzed step by step.
  • #1
qpham26
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Homework Statement



Given: The power absorbed by the 15 ohm resistor is 15 W. Find R.

http://sphotos-a.xx.fbcdn.net/hphotos-snc7/384382_495043340515186_1992745410_n.jpg

Homework Equations



parallel circuit for 2 resistor: Req =R1R2/ R1+R2

Voltage Division Rule: for series circuit VR2 = VsR2/(R1+R2)

The Attempt at a Solution


P = V2/R
P = 15W, R = 15Ω
P at 15Ω = 15 W => V at 15Ω = 15V

=> V at R = 25V - 15V = 10V

So I go around the circuit from the left to right.

Start at the double 4Ω => Req = 2Ω
the 2Ω + 6Ω || 24Ω => Req = 6Ω
6Ω+4Ω || 15Ω => Req = 6Ω

now the circuit only have R and the 6Ω

apply VR2 = VsR2/(R1+R2)
Plug in the number
solve for R = 4Ω

Please let me know if this is the right approach or if I have made a mistake.
Thanks for your time.
 
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  • #2
Both the approach and the answer look ok to me.
 
  • #3
answer is correct.
 

FAQ: Circuit with Series and parallel resistors, voltage division rule

1. What is a circuit with series and parallel resistors?

A circuit with series and parallel resistors is a combination of both series and parallel circuits. In this type of circuit, some resistors are connected in series, meaning they are connected one after the other, while others are connected in parallel, meaning they have a common connection point.

2. How is the voltage divided in a circuit with series and parallel resistors?

The voltage division rule states that the voltage across each resistor in a series circuit is proportional to its resistance. In a parallel circuit, the voltage across each resistor is equal to the total voltage of the circuit. Therefore, the voltage is divided between the resistors based on their individual resistances.

3. How do I calculate the total resistance in a circuit with series and parallel resistors?

To calculate the total resistance in a circuit with series and parallel resistors, you can use the following formula: 1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn. Simply add the reciprocals of each individual resistance and then take the reciprocal of the sum to find the total resistance.

4. What is the difference between a series and parallel circuit?

In a series circuit, the components are connected one after the other, creating a single pathway for current to flow. In a parallel circuit, the components have multiple pathways for current to flow. In terms of voltage, the voltage in a series circuit is divided between the components, while in a parallel circuit, each component has the same voltage as the source.

5. How do I calculate the voltage drop across a resistor in a circuit with series and parallel resistors?

To calculate the voltage drop across a resistor in a series circuit, you can use Ohm's law: V = IR, where V is the voltage drop, I is the current, and R is the resistance. In a parallel circuit, the voltage drop across each resistor is equal to the total voltage of the circuit. You can also use the voltage division rule to calculate the voltage drop across each resistor in a series-parallel circuit.

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