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A route for the flow of electricity that has elements of both parallel and series circuits.PowerPoint Presentation

A route for the flow of electricity that has elements of both parallel and series circuits.

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### A route for the flow of electricity that has elements of both parallel and series circuits.

- The first step is to simplify the circuit by making the parallel resistors into a single resistance.
- Resistance in parallel can be calculated by
1 / Rpar = 1 / R1 + 1 / R2 + 1 / R3 + ...

The new resistance is found to be

(1/(8+8) + ¼)^-1 = 3.2 Ohms

The new resistance is found to be

(1/6 + ¼ + ¼ + 1/3)^-1 = 1 Ohm

- Now label the currents throughout your circuit parallel resistors into a single resistance.
- Our simplified circuit now looks like this;

Loop 1 parallel resistors into a single resistance.

Loop 2

- In order to solve for the currents in each branch it is easiest to separate the two loops into individual loops and set up systems

Loop 2 parallel resistors into a single resistance.

Loop 1

- Now, using Ohm’s Law (V=IR), we can set up systems to solve for I1 and I2

10 = I2(13 + 7 +12 + 3.2 + 6) - 6I1

10 = I1(1 + 6) - 6I2

10 = 41.2I2 - 6I1

10 = 7I1 - 6I2

Now we use algebra to solve the systems for parallel resistors into a single resistance.I1 and I2

10 = 7I1 - 6I2

10 = -6I1 + 41.2I2

x6(10 = 7I1 + 6I2)

=60 = 42I1 +36I2

x7(10 = 6I1 + 41.2I2)

= 70 = -42I1 + 288.4I2

60= 42I1 +36I2

70 = -42I1 + 288.4I2

130 = 324.4I2I2 = .401 A

10 = 7I1+ 6(.401) I1 = 1.085 A

- Now we can find the current in each resistor parallel resistors into a single resistance..
- Since we know that in series the current stays the same we have the current for almost all the resistors, the tricky part comes with the resistors in parallel.
- Let’s de-simplify our parallel resistors and solve for the current in each branch!

3.2 Ohms parallel resistors into a single resistance.

1 Ohm

The original parallel systems are shown above, as well as their simplified resistance values. Using Ohm’s law, and the calculated I1 and I2, we can find the total voltage in each parallel system.

V=IR

V1 = 1.085*1 = 1.085 V

V2 = .401*3.2 = 1.283 V

3.2 Ohms parallel resistors into a single resistance.

1.283 V

1 Ohm

1.085 V

Now, knowing that voltage is equal in all branches in parallel, as well as knowing the value for each resistor, we can calculate the current travelling through each resistor through Ohm’s law.

R1 =1.085 = I*6Ω I = .181

R2 = 1.085=I*4Ω I = .271

R3 = 1.085= I*3Ω I = .362

R4 = 1.085= I*4Ω I = .271

R5 = 1.283= I*4Ω I = .321

R6 = 1.283= I*16Ω I = .080

Since we know current stays constant through series circuits we know the value of the current through R8, R9, and R10. Being the value of I2, .401 A. For R11, however, it is shared by both loops, thus both currents must be accounted for. I1 is stronger than I2 and they are travelling in opposite directions, because of this you must subtract I2 from I1, getting a value of .882 A.

Summary: we know the value of the current through

R7 = .040 A

R8 = .401 A

R9 = .401 A

R10 = .401 A

R11 = .882 A

R1 = .181 A

R2 = .271 A

R3 = .362 A

R4 = .271 A

R5 = .321 A

R6 = .040 A

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