Parallel resistanee is reciprocal of the sum?

• Lokhtar
In summary, the total resistance in a parallel circuit is found by taking the reciprocal of all individual resistances and adding them together. This can be derived from the equation V=IR and the definition of parallel resistance.
Lokhtar

Homework Statement

Why is parallel resistance the reciprocal of all individual resistances?

V=IR

The Attempt at a Solution

Well, since V is constant and I is different, you can write it as I=V/R, and since V won't change, you can make it I=V*(1/R1+1/R2),etc. So I get that, but why do you then have to take the reciprocal of all the resistances to get the total resistance? Wouldn't it just be the direct sum of the individual 1/Rs??

Lokhtar said:

Homework Statement

Why is parallel resistance the reciprocal of all individual resistances?

V=IR

The Attempt at a Solution

Well, since V is constant and I is different, you can write it as I=V/R, and since V won't change, you can make it I=V*(1/R1+1/R2),etc. So I get that, but why do you then have to take the reciprocal of all the resistances to get the total resistance? Wouldn't it just be the direct sum of the individual 1/Rs??

Because, by definition, $I = V/R_{eq}$. So setting this equal to your expression, we get

$$\frac{1}{R_{eq}} = \frac{1}{R_1 + R_2 + \ldots}$$

The reason why parallel resistance is the reciprocal of all individual resistances is because of the way current flows in parallel circuits. In a parallel circuit, the current is divided among the different branches, and the total current is equal to the sum of the currents in each branch. This means that the total current is inversely proportional to the total resistance, as seen in the equation I=V/R. So, in order to calculate the total resistance, we need to take the reciprocal of all the individual resistances, which represents the inverse relationship between current and resistance in parallel circuits. In other words, the more resistors you add in parallel, the lower the total resistance will be, since the current is divided among more branches. This is why parallel resistance is the reciprocal of all individual resistances.

1. What is parallel resistance?

Parallel resistance is a type of electrical resistance that occurs when there are multiple electrical pathways for current to flow through a circuit. In other words, the circuit branches into different paths and the total resistance is less than if the components were connected in series.

2. What does it mean for parallel resistance to be reciprocal?

Reciprocal in this context means that the total resistance of a parallel circuit is equal to the reciprocal of the sum of the individual resistances. In other words, if you add the reciprocals of each individual resistance, you will get the total resistance of the parallel circuit.

3. Why is parallel resistance important?

Parallel resistance is important because it allows for more efficient current flow in a circuit. By dividing the current into different paths, the overall resistance decreases, leading to a higher current flow and less power loss.

4. How do you calculate parallel resistance?

The formula for calculating parallel resistance is: 1/Rt = 1/R1 + 1/R2 + ... + 1/Rn, where Rt is the total resistance and R1, R2, etc. are the individual resistances. To find the total resistance, take the reciprocal of the sum of the individual resistances.

5. What are some real-life applications of parallel resistance?

Parallel resistance is commonly used in household wiring, where multiple appliances are connected to the same power source. It is also used in electronic circuits, such as in computers and televisions, to allow for efficient current flow. Additionally, parallel resistance is used in power grids to distribute electricity to different areas.

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