3-1

Electrical Circuit Calculations

Individual electrical circuits normally combine one or more resistance or load devices. The design

of the electrical circuit will determine which type of circuit is used. There are three basic types of

circuits: the series circuit, the parallel circuit, and the series-parallel circuit.

Series Circuit Calculations

A series circuit is a circuit in which a given current begins at the voltage source, passes through

each electrical device in a single pathway, before returning to the voltage source. In calculating

values for current, voltage, power and resistance, the following rules apply...

Rule #1: Current (Amps)

The current remains the same throughout a series circuit.

Rule #2: Voltage (EMF)

The total voltage of a series circuit equals the total of all of the voltages of the resistors

in the circuit added together.

Rule #3: Power (Watts)

The total power of a series circuit equals the total of all of the wattages of the individual

resistors in the circuit.

3-2

Rule #4: Resistance (Ohms)

The total resistance of a series circuit equals the total all of the resistances added together.

Series Circuit Example

The great thing about using the Ohm's Law Ladder is that we can set one up at any point of a

series or parallel circuit. In the series circuit above we have set up ladders at each resistor and the

totals at the power supply.

In the circuit below our power supply (battery) has a total of 12 watts

(W)

of power, 12 volts

(E)

, 1

amp

(I)

, and 12 ohms of resistance

(R)

. By applying the four series circuit rules we find that our

current

(I)

= 1 amp) is the same everywhere in the circuit. This is due to the fact that all of the

electrons (current flow) that leave the power source return back to the source eventually. The sum

total of watts, volts, and resistance can be found by finding the totals of each.

Resistance:

The sum total of a series circuit equals the total all of the resistances added together.

Total Resistance = 12 (2 + 4 +6)

Current:

remains the same throughout the circuit. Now that we know that there is 1 Amp at the

power supply we know that there is 1 Amp

(I)

everywhere in the circuit. The sum total Volts

(I)

=

12, and total total Resistance

(R)

= 12, we can find amps at the power source.

12 Volts / 12 Ohms = 1 Amp

Voltage:

The total voltage of a series circuit equals the total of all of the voltages of the resistors in

the circuit added together.

3-3

Total Volts = 12 (2 + 4 +6)

Watts (Power):

the total of a series circuit equals the total of all of the wattages of the resistors in

the circuit added together.

Total Watts = 12 (2 + 4 +6)

Don't forget...

•

Current remains the same throughout the circuit.

•

Watts, Volts and Resistance are all additive. They can all be added together to get the total.

Parallel Circuit Calculations

A parallel circuit is a circuit in which the current branches out so that only part of the current

beginning at the voltage source passes through each resistor. In calculating values for voltage,

current, power and ohms, the following rules apply:

Rule #1: Voltage (EMF)

The voltage remains the same throughout a parallel circuit.

Rule #2: Current (Amps)

The total current of a parallel circuit equals the total of all of the currents of the resistors in the

circuit added together.

Rule #3: Power (Watts)

The total power of a parallel circuit equals the total of all of the wattages of the resistors in the

circuit added together.

+

+

+

W

E

I

R

4

W

E

I

R

W

E

I

R

12

2

W

E

I

R

6

12

12

12

3-4

Rule #4: Resistance (Ohms)

The total resistance in a parallel circuit must use the following formula due to the fact that the

current branches out into each resistor simultaneously.

1

Total Resistance =

1

1

1

R1 + R2 + R3...

Parallel Circuit Example

Let's try the Ohm's Law Ladder on a parallel circuit. We have set up ladders at each resistor (#1,

#2, #3), and the totals at the power supply. Notice that all known resistor values have been placed

by their respective variables: Total E = 12, R#1 = 2, R#2 = 4, R#3 = 6. Applying the four Parallel

circuit rules we find...

Voltage

The voltage remains the same throughout the circuit.

Current:

The total current of a parallel circuit equals the total of all of the current of the resistors in

the circuit added together.

Total Current = 6 + 3 + 2

Total Current = 11

+

+

+

W

E

I

R

4

W

E

I

R

W

E

I

R

12

2

W

E

I

R

6

12

12

12

6

3

2

11

+

+

+

W

E

I

R

4

W

E

I

R

W

E

I

R

12

2

W

E

I

R

6

12

12

12

6

3

2

11

24

36

72

132

1.09

3-5

Power:

total of a parallel circuit equals the total of all of the wattages of the resistors in the circuit

added together.

"

Total Watts = 72 + 36 + 24

"Total Watts = 132

Resistance:

total of a parallel circuit equals the total of all the voltages divided by the total of all

the amperages.

Total Resistance =

Total Volts_

Total Amps

Total Resistance = 12 / 11

Total Resistance = 1.09

That's a lot easier than this old formula...

"

1

"Total Resistance =

1

1

1

"" 2 + 4 + 6

+

+

+

W

E

I

R

4

W

E

I

R

W

E

I

R

12

2

W

E

I

R

6

12

12

12

6

3

2

11

24

36

72

132

1.09

3-6

Series-Parallel Circuits

It is possible to combine series and parallel circuits in order to alter voltages, using series circuits,

or currents, using parallel circuits, to meet various load requirements. In solving series-parallel

calculations you must first separate the circuit into its series and parallel parts. Each part of the

circuit can be solved separately through common resistors.

In calculating the parallel section, all of the parallel circuit rules apply; voltage remains the same

throughout the circuit, current, and wattage are additive. What if we find the total resistance in this

problem.

We could use this formula...

"

1

"

Total R =

1

1

" R1 + R2

Or, here’s an alternate formula...

"Total R = __

R3 x R4

__

" "R3 + R4

"Total R =

4 x 4

__

""4 + 4

Was your answer for total resistance 2 ohms ? Now that we know that the total resistance of the

two 4 ohm resistors could we replace them with one 2 ohm resistor ?

+

+

+

W

E

I

R

W

E

I

R

12

2

W

E

I

R

2

+

+

+

W

E

I

R

4

W

E

I

R

W

E

I

R

12

4

W

E

I

R

2

3-7

Now, calculating the rest of the problem is the same as calculating a series circuit with two

resistors. Resistance total for a series circuit is additive.

R Total = R#1 + R#2 + R#3

R Total = 2 + 2

R Total = 4 ohms

Series-Parallel Tip:

Always start at the resistor farthest away from the power source then work

back.

3-8

Electrical Circuit Problems

1."In a series circuit _______.

"(a)"voltage is common"(c)"current is common"

"(b)"wattage is commom"(d)"resistance is common

2."Four batteries connected in series will provide _______ volts if each is 1-1/2 volts.

"(a)"1-1/2"(c)"6

"(b)"4"(d)"8

3."Three 9 ohm resistors connected in parallel have a total resistance of _______ ohms.

"(a)"27"(c)"3

"(b)"9"(d)"1.5

4."Two resistors, a 4 ohm and an 8 ohm, are in series. The total voltage drop across both resistors is

"12 volts. What is the current through the 4 ohm resistor ?

"(a)"1 amp"(c)"4 amps

"(b)"2 amps"(d)"8 amps

5."Two 500 watt lamps are connected in series across a 110 volt line drawing 2 amps. The total

"power consumed is ?

"(a)"1,000 watts"(c)"220 watts

"(b)"250 watts"(d)"55 watts

6."Four heater coils will consume the most power (watts) when connected ____.

"(a)"all in series"(c)"2 parallel pairs in series

"(b)"all in parallel"(d)"2 in parallel, two in series

7."What is the total resistance in this series-parallel circuit ?

"(a)"42 Ω"(c)"17.5 Ω

"(b)"4.3 Ω"(d)"20 Ω

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