Parallel Circuits Explained: Voltage, Current, and Resistance in Parallel

In this Engineering Mindset video, parallel circuits are dissected to show how voltage is the same across all branches while current splits among paths. The lesson covers how to use Ohm's law in parallel, how to determine total current, how branch resistance affects currents, and how to calculate the total resistance in a parallel network. The presenter walks through representative examples with lamps and batteries, explains the concept of conductance, and ends with practice problems to test understanding.

Introduction to Parallel Circuits

Engineering Mindset investigates parallel circuits to explain how components wired in parallel share the same voltage across each branch while the available current divides between paths. The video emphasizes the distinction between series and parallel wiring, noting that parallel paths provide redundancy so a single faulty path does not stop the entire circuit. Electron flow is discussed in the context of both conventional and electron flow models, with a reminder that the measured quantity is the difference in potential between two points.

Voltage in Parallel

The video demonstrates that in parallel circuits the voltage across each branch equals the battery voltage. This is explained using a simple tank analogy where voltage is like water pressure. Since every branch connects directly to the battery’s terminals, each component experiences the full voltage, regardless of the number of branches.

Current Flow and Division

Current is described as the flow of electrons and is measured in amperes. When resistors are placed in parallel, the total current increases with more branches, while the current through each branch remains determined by its own resistance and the applied voltage. The video provides examples where two 1 ohm lamps in parallel connected to a 1.5 V battery yield a total current of 3 A, with each lamp carrying 1.5 A. The wire between branches also carries 1.5 A, illustrating how current splits and rejoins.

Ohm's Law in Parallel

Ohm's law is introduced as I = V / R for each branch. If a 1.5 V source drives a 1 ohm lamp, the branch current is 1.5 A. Adding a second identical branch doubles the total current to 3 A, while each branch still carries 1.5 A. This highlights how total current is the sum of branch currents in parallel circuits.

Total Current and Branch Currents

The total current equals the sum of currents in all branches. If one branch’s resistance changes, branch currents adjust accordingly, affecting the total current. A modified scenario shows a 2 ohm lamp in one branch reduces the current through that branch to 0.75 A while the second lamp maintains 1.5 A, and the overall current drops to 2.25 A. Adding a third 1 ohm lamp in parallel increases the total current to 4.5 A with each lamp seeing 1.5 A, while currents in the wires between lamps adjust to reflect the new distribution.

Total Resistance in Parallel

The video explains the key formula for parallel resistance RT = 1 / (1/R1 + 1/R2 + ...). This reciprocal approach reflects how multiple paths reduce the overall resistance. Examples show why two 10 ohm resistors in parallel yield RT = 5 ohms, and other combinations like 10 ohm, 5 ohm, and 2 ohm in parallel yield RT = 1.25 ohms. A conductance perspective is used to justify the reciprocal form, noting that total conductance is the sum of branch conductances, with RT = 1 / Gtotal.

Power in Parallel Circuits

Power is addressed using either P = V^2 / R or P = VI. With a 6 V source across a 10 ohm resistor, P = 3.6 W, while a 5 ohm resistor carries 7.2 W, and the total power is 10.8 W in the example with two parallel resistors. The video shows that total power can also be found by multiplying the total current by the voltage or by summing branch powers. This section ties together current, voltage, resistance, and power in parallel networks.

Practice Problems and Hands-On Calculations

The instructor invites viewers to solve problems involving multiple resistors in parallel, total current calculations, and determining unknown branch currents and resistances given total current and some branch data. The problems reinforce the concept that parallel circuits share voltage, current divides according to branch resistance, and total resistance is calculated via the reciprocal formula. Solutions and further explanations are provided via links in the description.

Takeaway and Tools

The video concludes with encouragement to use a free parallel resistance calculator to verify results and to revisit the related videos on Ohm's law and series-parallel combinations for a broader understanding of circuit analysis.