# Parallel circuit Definition and 21 Discussions

Two-terminal components and electrical networks can be connected in series or parallel. The resulting electrical network will have two terminals, and itself can participate in a series or parallel topology. Whether a two-terminal "object" is an electrical component (e.g. a resistor) or an electrical network (e.g. resistors in series) is a matter of perspective. This article will use "component" to refer to a two-terminal "object" that participate in the series/parallel networks.
Components connected in series are connected along a single "electrical path", and each component has the same current through it, equal to the current through the network. The voltage across the network is equal to the sum of the voltages across each component. Components connected in parallel are connected along multiple paths, and each component has the same voltage across it, equal to the voltage across the network. The current through the network is equal to the sum of the currents through each component.
The two preceding statements are equivalent, except for exchanging the role of voltage and current.
A circuit composed solely of components connected in series is known as a series circuit; likewise, one connected completely in parallel is known as a parallel circuit. Many circuits can be analyzed as combination of series and parallel circuits, along with other configurations.
In a series circuit, the current that flows through each of the components is the same, and the voltage across the circuit is the sum of the individual voltage drops across each component. In a parallel circuit, the voltage across each of the components is the same, and the total current is the sum of the currents flowing through each component.Consider a very simple circuit consisting of four light bulbs and a 12-volt automotive battery. If a wire joins the battery to one bulb, to the next bulb, to the next bulb, to the next bulb, then back to the battery in one continuous loop, the bulbs are said to be in series. If each bulb is wired to the battery in a separate loop, the bulbs are said to be in parallel. If the four light bulbs are connected in series, the same current flows through all of them and the voltage drop is 3-volts across each bulb, which may not be sufficient to make them glow. If the light bulbs are connected in parallel, the currents through the light bulbs combine to form the current in the battery, while the voltage drop is 12-volts across each bulb and they all glow.
In a series circuit, every device must function for the circuit to be complete. If one bulb burns out in a series circuit, the entire circuit is broken. In parallel circuits, each light bulb has its own circuit, so all but one light could be burned out, and the last one will still function.

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1. ### R_th wrong while applying series and parallel simple theory

Summary:: Trying to find Rth but I do not get the same value as the one from the solution. [moderator: moved from a technical forum. No template.] I am trying to find Rth to solve this problem, however once I simplified it, I get a value of 700.745 Ω while in the solution, the answer is...
2. ### How does the current divide in parallel inductors?

I apologize using English fluently because I am not an Enlgish speaker. When I tried to solve this problem, I used current divider rule. So, $$i_o(t) = \frac{3}{3+5}*4e^{-2t} = 1.5*e^{-2t} A$$ However, This was wrong. The answer is $$1.5*e^{-2t} + 0.5 A$$ If I use $$V_O = L*\frac{di}{dt}$$...
3. ### Current through source in AC circuit with R & LC in parallel

Homework Statement In the circuit diagram shown , Xc = 100 ohm , XL = 200 ohm , R = 100 ohm , the effective current through the source is ? Homework Equations Z= √( R^2 + ( XL - Xc)^2) Vrms = Irms/ Z The Attempt at a Solution I tried to draw the phaser diagram and calculate the relation...
4. ### Why does current choose the short circuit path?

I've seen answers saying that electricity takes path of least resistance, I know this and there is no need to explain this for me. A forum's answer told me that the electrons initially flow through to the path with resistance and eventually becomes congested (redirecting the remaining electrons...
5. ### Potential Divider Circuit

Homework Statement Homework Equations The Attempt at a Solution When we will move the contact X towards P, the potential difference should be maximum across the potential divider. I work out A as my answer but I think it is wrong.
6. ### Parallel and Series Circuit

Homework Statement I'm asked to find a combination of resistors (parallel and/or series) that uses resistors of 25 Ω, 100 Ω, 50 Ω, and 50 Ω. They should add up to give a total resistance of 62.5 Ω. Homework Equations Req for parallel = 1/R1 + 1/R2 + ... Req for series = R1 + R2 + ... The...
7. ### Engineering Electrical circuits: when all switches are closed, what is R?

Homework Statement https://pasteboard.co/Hj3g5Km.jpg When both switches 1 and 2 are closed,what is the total resistance of the set up? I couldn't figure out which resistors are connected in parallel and which resistors are actually in series in this set up when both swtiches are closed. I...
8. ### Current Dividing in an Electrical Circuit

A circuit contains a 7.5V d.c power supply and three resistors. The total resistance of the circuit is 30 ohms. Why will the largest current in the 18 ohm resistor? As far as I know is that the smallest current will be in 60 ohm resistor because it has the maximum resistance. Please explain...
9. ### What's the total resistance in this circuit?

Homework Statement https://imgur.com/3H3pCkD R is the resistance of each resistor, determine total resistance in the circuit. (see the image in the link above) Homework Equations R=1/R₁+1/R₂+1/R₃+... (in parralel circuit) R=R₁+R₂+R₃... (in series circuit) The Attempt at a Solution I'm...
10. ### Two like capacitors in parallel

I'm having a little trouble understanding capacitors in parallel and series. I understand that if there are two capacitors in a circuit with a potential difference Vab then the potential difference across the capacitors is also Vab. Every example I have seen have been for two capacitors with...
11. ### Can you help me find the current through the 15 Ohm resistor branch?

Homework Statement Homework Equations I = VR Series = current the same, voltage different Parallel = current different, voltage the same The Attempt at a Solution Is the 1 ohm and 15 ohm parallel? I'm still learning to differentiate it. If yes, then R = 15/16 ohm Is the R series to 5ohm? If...
12. ### Thevenin reduction of network for fault analysis trouble.

Homework Statement Reduction from top network to bottom network in the screen shot. I can not find the steps that have been taken to do this. Fault impedance = Zfa = Zfb = Zfc = j0.5 Homework Equations The Attempt at a Solution in hand written screenshot, sorry for the mess, just to show...
13. ### Series and Parallel Combination

[Note: Thread has been moved to the homework forums by a mentor] This is the Given problem This is my solution part 1 - What I did here is I series the R3 and R4 (R3 + R4), and I parallel the R34 to R5 (most of the calculation are from the calculator) This is my solution part 2 The...
14. ### Resistor parallel to short circuit when finding R_thev ....?

(sorry, I couldn't figure out how to insert an image from my drive) I have a problem where in finding the thevenin resistance I take out my independent sources and as a result I'm left with a resistor parallel to a short circuit. Should I ignore this resistor when calculating equivalent...
15. ### Solving voltage divider involving capacitors

Homework Statement Given ZV1 = ZV2 = 100Ω, ZCCV = ZCV = 2000/j = -2000j, and VV/VC = 0.04789. I'm trying to get the given VV/VC result. Homework Equations I know that 1/ZV = 1/ZV1 + 1/ZV2 + 1/ZCV VV = ZV / (ZV + ZCCV) * VC The Attempt at a Solution 1/ZV = 1/ZV1 + 1/ZV2 + 1/ZCV = 1/100 +...
16. ### LR circuit in parallel, need someone to check answer

Homework Statement L is a perfect inductor with inductance L. The switch is turned on at t=0 and the currents i1 and i2 run trhough the circuit as indicated by the figure. Homework Equations Given this circuit I need to find i1 and i2 for t=0 and t => infinity. The Attempt at a Solution For...
17. ### Parallel Buck Converters

I have a ton of 1A buck converters, and have a 5A application in which i need to run. I do not want to order any new buck converters, because I already have so many 1A ones, and do not have money for any new ones. Each one can only handle 1A before it over heats. I was wondering if I could use...
18. ### Potential difference of each resistor

Homework Statement What is the potential difference across each resistor? I know that I'll have to incorporate the V=iR equation but I don't know where to start though... My first attempt was with these: R1=4 R2=8 R3=5 R4=6 R5=3 24-I1R1-I1R2-I3R3+I4R4+I5R5=0 but this lead me nowhere so I...
19. ### Calculate the current between point A and B

Homework Statement [/B] What is the current between points A and B? The current I is unknown. The voltage is 12V. R1 = 3 Ohm R2 = 6 Ohm R3 = R4 = 4 Ohm Homework Equations U= R*I The Attempt at a Solution Total resistance from both branches: 1/R = 1/(R_1+R_3) + 1/(R_2+R_4) 1/R = 1/7 +...
20. ### Engineering Series and parallel circuit

Homework Statement Hello, can you help with this problem. For the next circuit, determine the voltages Homework Equations I=V/RT RT=R1+R2+R3+...+Rn P=V^2/R V=V1=V2=V3 I=V/R GT=1/R1+1/R2+1/R3+...+1/Rn The Attempt at a Solution My background is that I only know a very few and I don´t know how to...
21. ### Engineering Parallel circuit problem

Homework Statement Solve the next circuit to find the voltages Homework Equations I=V/R GT=(1/R1)+(1/Rn) V=V1=V2=V3 The Attempt at a Solution My background is that I know that in a parallel circuit, the voltage for each component is the same and electric current it's equal to the sum of the...