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Parallel Problem Solutions

Problem #1

        The first step is to find the current flowing in each branch of the circuit:

Et = E1=E2=E3=E4 = 12 volts (all voltages are equal to the source voltage in parallel)

I1= E1/R1
I1 = 12 volts/ 12 ohms = 1 amp

I2 = E2/R2
I2 = 12 volts/ 3 ohms = 4 amps

I3 = E3/R3
I3 = 12 volts/ 6 ohms = 2 amps

I4 = E4/R4
I4 = 12 volts/ 2 ohms = 6 amps

It = I1+I2+I3+I4
It = 1 amp + 4 amps + 2 amps + 6 amps = 13 amps

Problem #2

     Et = E1 = E2 = E3 = 12 volts

I1 = E1/R1
I1 = 12 volts/ 2 ohms = 6 amps

I2 = E2/R2
I2 = 12 volts/ 6 ohms = 2 amps

I3 = E3/R3
I3 = 12 volts/ 3 ohms = 4 amps

Problem #3

Et = E1 = E2 = 12 volts

I1 = E1/R1
I1 = 12 volts/ 1 ohm = 12 amps

I2 = E2/R2
I2 = 12 volts/ 24 ohms = 0.5 amps

It = I1+I2
It = 12 amps + 0.5 amps = 12.5 amps

Both ammeters are located so that total circuit current will flow
through each ammeter - therefore they will both read
total circuit current - or 12.5 amps.

Problem #4

     Finding resistance using the inverse formula:

         Problem #1

1/Rt = 1/R1 + 1/R2 + 1/R3 + 1/R4
1/Rt = 1/12 + 1/3 + 1/6 + 1/2

            Using a common denominator of 12:

1/Rt = 1/12 + 4/12 + 2/12 + 6/12
1/Rt = 13/12
Rt = 12/13 = 0.923 ohms

            Problem #2

1/Rt = 1/R1 + 1/R2 + 1/R3
1/Rt = 1/2 + 1/6 + 1/3

            Using a common denominator of 6:

1/Rt = 3/6 + 1/6 + 2/6
1/Rt = 6/6
Rt = 1.0 ohms

           Problem #3

1/Rt = 1/R1 + 1/R2
1/Rt = 1/1 + 1/24

            Using a common denominator of 24:

1/Rt = 24/24 + 1/24
1/Rt = 25/24
Rt = 24/25
Rt = 0.96 ohms

         Finding resistance using the voltage method:

          Problem #1

Rt = Et/It
Rt = 12 volts/ 13 amps = 0.923 ohms

         Problem #2

Rt = Et/It
Rt = 12 volts/ 12 amps = 1.0 ohms

          Problem #3

Rt = Et/It
Rt = 12 volts/ 12.5 amps = 0.96 ohms

Now - let's go back and look at the last problem in the series section  - the Complex Circuit:

In the first branch, there are two resistors in series.  To find the total of these, just add
them together:

Rt = 17 ohms + 7 ohms = 24 ohms

The current flow through this branch can be found:

It = Et/Rt
It = 12 volts/ 24 ohms = 0.5 amps

The voltage drop at V1 can now be found:

E1 = I1 x R1
E1 = 0.5 amps x 17 ohms = 8.5 volts (V1)

The voltage drop at V2 can now be found:

E2 = I2 x R2
E2 = 0.5 amps x 7 ohms = 3.5 volts (V2)

The voltage drop at V3 would equal the source voltage:

E3 = 12 volts (V3)


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