Question about Finding unknown resistance by Ohms and Kirchoff's Laws

In summary, the unknown resistance Rx can be found by using Ohm's and Kirchoff's Rules. By applying the formula V = IR, the voltage across the 2 ohm resistor was determined to be 4 V. However, the logic used to determine the voltage across the two upper resistors in parallel needs to be revised. Kirchoff's Current Law was then applied at the nodes to calculate the current. Finally, Ohm's Law was used to find the resistance Rx, but the resulting value was incorrect.
  • #1
Orellanal
1
0

Homework Statement



Using Ohm's and Kirchoff's Rules find the unknown resistance Rx

Homework Equations



V = IR

Sum of currents at a node is zero
Sum of voltages around a loop is zero

The Attempt at a Solution




For the 2 ohm resistor I found the voltage to be 4V by the formula V = IR or V = 2A * 2ohm = 4 V
Therefore for the Rx resistor the voltage must also be 4 V as is it connected to the 2 ohm resistor in parallel.

The 4 and the 8 ohm resistors on top are connected in parallel and therefore must have the same voltage. 12 V - 8 V on the bottom two resistors gives 4 V for them which means that the voltage through each of the top resistors must be 2 V. Knowing this I then took Kirchoff's Current law at the nodes.

Node 2 (Right)

2V/ 8 ohm = 0.25 A (going into the node)

- 0.25 A + 2A = -1.75 A (going into the node)


Node 1 (Left)

-.5 A (into the node) + 1.75 A (going out of the node) = 1.25 A (going out of the node)

I then used ohm's law to find the resistance x by V = IR --> R = V/I or 4V/ 1.25 A = 3.2 ohms
which is wrong.

I thank you in advance for your help.
 

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  • #2
Orellanal said:

Homework Statement



Using Ohm's and Kirchoff's Rules find the unknown resistance Rx

Homework Equations



V = IR

Sum of currents at a node is zero
Sum of voltages around a loop is zero

The Attempt at a Solution




For the 2 ohm resistor I found the voltage to be 4V by the formula V = IR or V = 2A * 2ohm = 4 V
Therefore for the Rx resistor the voltage must also be 4 V as is it connected to the 2 ohm resistor in parallel.
Good so far!

The 4 and the 8 ohm resistors on top are connected in parallel and therefore must have the same voltage. 12 V - 8 V on the bottom two resistors gives 4 V for them which means that the voltage through each of the top resistors must be 2 V.
You'll want to revisit that logic. Yes, the two upper resistors are in parallel. Being in parallel they will share the same potential drop across them (voltage is across a component, current goes through a component). You determined that the voltage across the two lower resistors is 4 V. What does that leave (of the supply potential's 12 V) to appear across both of those upper resistors?

Knowing this I then took Kirchoff's Current law at the nodes.

Node 2 (Right)

2V/ 8 ohm = 0.25 A (going into the node)

- 0.25 A + 2A = -1.75 A (going into the node)


Node 1 (Left)

-.5 A (into the node) + 1.75 A (going out of the node) = 1.25 A (going out of the node)

I then used ohm's law to find the resistance x by V = IR --> R = V/I or 4V/ 1.25 A = 3.2 ohms
which is wrong.

I thank you in advance for your help.
 

Related to Question about Finding unknown resistance by Ohms and Kirchoff's Laws

1. How do I use Ohm's Law to find an unknown resistance?

To find an unknown resistance using Ohm's Law, you will need to know the voltage and current values in the circuit. Then, simply divide the voltage by the current to get the resistance value (R=V/I).

2. Can Kirchoff's Laws be used to find an unknown resistance?

Yes, Kirchoff's Laws can be used to find an unknown resistance. By applying Kirchoff's Voltage Law (KVL) and Kirchoff's Current Law (KCL) to the circuit, you can set up a system of equations that can be solved to find the unknown resistance.

3. How do I apply Kirchoff's Laws to a circuit?

To apply Kirchoff's Laws to a circuit, first identify all the different loops in the circuit and assign a direction to each one. Then, use KVL to set up an equation for each loop, and use KCL to set up an equation for each node. Finally, solve the system of equations to find the unknown resistance.

4. Are there any limitations to using Ohm's Law and Kirchoff's Laws to find an unknown resistance?

Yes, there are some limitations to using Ohm's Law and Kirchoff's Laws. These laws assume that the circuit is in a steady state and that all components are linear and obey Ohm's Law. In real-world circuits, there may be non-linear components or the circuit may not be in a steady state, which can affect the accuracy of the calculations.

5. Can I use Ohm's Law and Kirchoff's Laws to find an unknown resistance in a complex circuit?

Yes, you can use Ohm's Law and Kirchoff's Laws to find an unknown resistance in a complex circuit. However, in complex circuits, it may be more challenging to identify all the loops and nodes and set up the equations. It may also be necessary to use additional circuit analysis techniques, such as Thevenin's or Norton's theorem, to simplify the circuit before solving for the unknown resistance.

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