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| 184_notes:examples:week8_resistors_parallel [2021/06/28 23:45] – schram45 | 184_notes:examples:week8_resistors_parallel [2021/06/28 23:51] (current) – [Solution] schram45 | ||
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| ===Approximations & Assumptions=== | ===Approximations & Assumptions=== | ||
| - | * The wire has very very small resistance when compared to the other resistors in the circuit: This means the wires will have no potential difference across them in our model. | + | * The wire has very very small resistance when compared to the other resistors in the circuit: This allows there to be no energy loss across |
| - | * The circuit is in a steady state: It takes a finite amount of time for the circuit to set up a charge gradient | + | * The circuit is in a steady state: It takes a finite amount of time for a circuit to reach steady state and set up a charge gradient. |
| - | * Approximating the battery as a mechanical battery. | + | * Approximating the battery as a mechanical battery: This means the battery will supply a steady power source to the circuit to keep it in steady state. |
| - | * The resistors in the circuit are made of Ohmic materials. | + | * The resistors in the circuit are made of Ohmic materials: Ohmic materials have a linear relationship between voltage and current, this allows us to use ohms law. |
| ===Representations=== | ===Representations=== | ||
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| We know enough potential differences to find the voltage across Resistor 2: | We know enough potential differences to find the voltage across Resistor 2: | ||
| $$\Delta V_2 = \Delta V_3+\Delta V_4 = 8 \text{ V}$$ | $$\Delta V_2 = \Delta V_3+\Delta V_4 = 8 \text{ V}$$ | ||
| + | One way in which we can evaluate the solution here is to pick a few other loops in the circuit and make sure they are still valid. There are often times many more loops in a circuit than the solution goes through. | ||
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| That's all! Note that there are a lot of ways to do this problem, but we chose an approach that showcases the power of knowing equivalent resistance for resistors in parallel, and the power of the Loop Rule. See if you can create a different method for finding the unknowns. | That's all! Note that there are a lot of ways to do this problem, but we chose an approach that showcases the power of knowing equivalent resistance for resistors in parallel, and the power of the Loop Rule. See if you can create a different method for finding the unknowns. | ||