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### Course: Class 10 Physics (India)>Unit 3

Lesson 5: Series and parallel resistors

# Parallel resistors (derivation)

Discover the fascinating world of parallel resistors in electrical circuits! Learn how to identify parallel resistors, understand the concept of shared nodes and voltage, and apply Ohm's law to calculate equivalent resistance. Master the formula for parallel resistors and enhance your circuit analysis skills with real-life examples. Created by Willy McAllister.

## Want to join the conversation?

• May be asking this question prematurely, but the obvious questions is this: why does the net resistance actually DECREASE when using 2 resistors in parallel?
• Think of it this way, imagine you are in a supermarket and a bunch of people want to check stuff out. If you only have one cashier, the lines going to go pretty slowly. But if you add another cashier, more people can get their stuff checked out and the line would go faster. The more cashiers you add, the faster the line will go. Parallel circuits work similarly. The more resistors you add, the more paths through which current can flow. Hope this helps!
• Hi, I know how to calculate resistors in parallel but I've never fully understood the math behind it. To be more specific, I don't understand why we take 1/R1 + 1/R2. Can anyone please explain this to me or link to a useful video? Thanks.
• Hello Ben,

Here you go - hot off the YouTube presses. In this video I show how the equation may be derived by analyzing the current in the circuit.

Regards,

APD
• I might just be misunderstanding something, but I always thought that the current took the path of least resistance, so if you have parallel resistors with different amounts of resistance such as at , wouldn't the current just choose the route with the 20 ohm resister?
• Imagine a narrow stream with water flowing. Drop a rock in the stream about 1/3 of the way from one edge. The water will split and flow around the rock on either side. The wide side corresponds to the lower resistor. Most, but not all, of the water goes on the wide side. There is always some that flows on the narrow (high resistance) side. Electric current does exactly the same thing.

If the rock is right in the center of the stream you would expect a 50-50 split of water on either side. If you move the rock slightly to one side you wouldn't expect all the water to suddenly 100% snap over to the slightly wider side.
• at , Willy said that current divides itself. since current don't have any brain it would divide itself in a random way. then how can we find the relation of division of current?
• A mental image that might help is to think of water flowing in a stream. If there is a rock in the stream, the water flow splits in two, with some flowing to one side of the rock and some flowing around the other side. The water doesn't have a brain, but the process is not random. The flow of electrical current splits in the same way. It is not random, because it is based on known principles. For resistors in parallel, that principle is Ohm's Law. If you know Ohm's Law, and you realize the voltage on the two resistors is the same, you can solve for both currents.
• How does sharing the same node mean sharing the same voltage?
• hi .
why did we take the voltage as V itself in finding parallel resistance whereas for finding series resistance , we took the voltage for each resistor as V1, V2, V3 etc. ?
• We should always take Voltage as V in parallel resistors and V1, V2 and V3 in Series.
We take it so because, voltage splits in series while the voltage is constant in parallel.
• At , what is the significance of using the reciprocal of 1/Rp when we established that i = V * (1/Rp)?
• Your point is valid; there is no mathematical need to work out R since we use the reciprocal directly in the next step to calculate i, the current. Taking the reciprocal is just a habit. I feel more comfortable knowing the resistance value as well as the 1/R value (the conductance). It is easier for me to notice an error if the resistance value is way off, compared to noticing an incorrect conductance (often a number way less than 1). Lots of engineers work with parallel circuits using conductance (1/R) values, it is a matter of personal choice.
• Why is voltage in a parallel circuit the same as the voltage of the source? I thought voltage was added up across components which would be equal to the voltage of the source.
• If you have two resistors in parallel that means their two terminals are tied together (perhaps think of the resistors as holding hands). There are only two wires. There can only be one voltage between two wires.

You are perhaps describing how the voltages add up for resistors in series.
(1 vote)

• shouldn't V * (1/R1 + 1/R2)
equal
V * 2/Rp?
because 1/n + 1/n = 2/n generally, or is it this way because you reduced it?