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## MCAT

### Course: MCAT>Unit 8

Lesson 11: Current and resistance

# Resistors in parallel

Explore the intriguing world of parallel resistors in circuits. Learn how current splits and combines in different branches, and how voltage remains constant across resistors. Uncover the formula for total resistance and apply it to solve real-world problems. Created by Sal Khan.

## Want to join the conversation?

• I have a very basic doubt.. its said that the current flowin through 2 resistances in series is same.. but shouldnt the initial current decrease after passing through an R, n decrease furthr on passing through the 2nd one??? • Its helpful to think of an analogy to visualize it better. Lets say you have a water pump (BATTERY) and it has the potential (lets call this the VOLTAGE) to pump out 100 gallons/sec through a uniform pipe with a 2.256 ft diameter. This diameter happens to give a Cross-Sectional Area of 4 pi ft^2. We connect this water pump to a uniform pipe, this time with a CS-Area of 2 pi ft^2, and it goes around in a complete loop, ending at the back of the water pump (thus completing a CIRCUIT). Assume there is no air in the pipes and the pipes are completely full of water. The rate at which the water goes around is called the CURRENT. If you were to examine different sections of the pipe you would find the avg current to be a constant 50 gallons/sec; notice the current decreased by half as CS-Area decreased by half (Also true for ELECTRICAL CURRENT). Now lets say we add a SERIES of restrictions, one after another. The first restriction is 1 pi ft^2 and a second is 1/2 pi ft^2. What happened to the flow of water? Well, the 1st restriction slows the current to 25 ft/s and the 2nd one slows it to 12.5 ft/s. What is the overall rate of the entire CURRENT? Believe it or not, its 12.5 ft/s no matter where you measure it. Even though it can go through the 1st at 25ft/s the water has to wait for the the 12.5 ft/s water to go through the 2nd resistive pipe. This is how my physics textbook explains Direct Current. The relationship of cross-sectional area also applies to many other aspects in engineering and science. Try to apply this analogy to parallel circuits and things will start to click.
• I'm confused at .. i1 = i1 + i2.. does he mean i1 = i2 + i3? and then he says i1 + i2 = i1 on the other side.. (the parallel currents are labelled i2 and i3 right? which do add up to i1 right) thanks in advance • what is the difference between Voltage and Voltage Drop ? // thanks in advance • To put simply Voltage is the amount of energy each coulomb (6.24*10^18 electrons) has and thus voltage equals to joules per coulomb. So whenever we talk about voltage, it is with respect to the circuit. The source of voltage comes from the battery

Voltage Drop is how much energy is lost when current goes through a component. it could be a resistor or the wire itself. The flow of electrons collides with the lattice of the material and some of its kinetic energy is converted to heat. The electron has lost energy and we call that the voltage drop.

There is a pretty cool law called kirchhoff law, where at the end of the circuit, the voltage must be 0 (i.e. voltage Drop = voltage) . This simply has to do with the principle of the conservation of energy. If you are interested just google kirchoff's law., electronics is very interesting.

I hope this helps, best of luck
• At in the video the resistance comes out to be 4 ohms. While the mathematics behind this makes perfect sense, the physics doesn't. The smallest resistor on the entire circuit is 5 ohms. I understand that most of the electrons will want to pass through this, but wouldn't that mean that the total resistance should never come out to be less than the smallest resistor? • At , can someone explain why there is less resistance when there are more resistors without using math? Thank you! • I cant understand why does the potential difference across resistors arranged in parallel are same?
and what exactly doe this potential drop signifies • i have a doubt that why it is said that the current flows from positive terminal to negative terminal but the electrons flows from negative terminal to positive terminal. • To avoid dealing with negative signs all the time, we define something called conventional current as a postive current and we say that it flows from positive to negative. Just pretend that there are positive charges that move in the opposite directions of the electrons. It makes no difference. Electrical engineers never worry about which way the electrons are going. They just deal with conventional current.
• I've always wondered this; with the equation 1/Rtotal = 1/R1 + 1/R2 + ... why can't you take the inverse of both sides and just get Rtotal = R1 + R2... like in a series circuit? Why doesn't that work out mathematically?
(1 vote) • It has to do with common denominators in fractions. If you have like in the example 1/20 + 1/5 = 1/Rtotal, 1/20 +1/5 is 5/20 reduced to 1/4. Then you can take the reciprocal of 1/Rtotal = 1/4 giving R total =4.

If you were to take the original formula and just invert it (like you are suggesting) to R total = R1 + R2 + R3 you would have R total= 20 +5 =25. Which is obviously wrong. Because R1 and R2 are different values, when adding them up as fractions of 1/R you have to find a common denominator.

Hope this helps!  