(G5C04) Series and Parallel Components

What is the total resistance of three 100-ohm resistors in parallel?

A. .30 ohms
B. .33 ohms
C. 33.3 ohms
D. 300 ohms

The General License Course section 6.3 is all about parallel and serial electronic components and the concept of equivalent component values.  Based on Kirchoff’s Laws for electrical current and voltage, multiple electronic components such as resistors, capacitors, and inductors arranged in either parallel or serial connections in a circuit may be “replaced” by a singular equivalent component. Multiple exam questions test your mathematical skill in calculating the value of the equivalent component, or put another way, the equivalent value provided by the multiple components.

Each of the three component types mentioned above may be arranged in either series or parallel connections, and one of two general equations applies for calculating the equivalent component value depending on which type of component and which type of connectivity is involved.  The calculations themselves are rather trivial once properly set up, so the real challenge of these questions boils down to applying the appropriate equation form among the six possible combinations of component and connectivity.

Let’s consider the two general forms of the two equations involved, using a generic “X” component indicator.  The X component in these equations may be replaced by R for resistance, C for capacitance, or L for inductance.  (In no way is X intended to imply reactance, in these cases.)

Sum of Components form:
$latex X_{total} = X_1 + X_2 + X_3 + \ldots X_n &s=2&bg=e5e6db$

Reciprocal of Reciprocals form:
$latex X_{total} = \frac{1}{ \frac{1}{X_1} + \frac{1}{X_2} + \frac{1}{X_3}… \frac{1}{X_n}}&s=2&bg=e5e6db$

So, which of these two equations applies to each of the six combinations of component and connection types?  Here’s how that shakes out:

Component Type

Connected in Series

Connected in Parallel

Resistor

Sum of Components

Reciprocal of Reciprocals

Inductor

Sum of Components

Reciprocal of Reciprocals

Capacitor

Reciprocal of Reciprocals

Sum of Components

Notice that resistors and inductors have identical equation form application, while capacitors are the opposite from those two.  Keep this table of relationships in mind and you can’t go wrong in applying the proper equation to the scenario defined in the exam question.  Additional memory aids, circuit illustrations, and examples are provided in the HamRadioSchool.com General License Course book, section 6.3.

Now, let’s apply the proper equation form to the question at hand, G5C04:  What is the total resistance of three 100-ohm resistors in parallel?  Here’s how that simple circuit arrangement may be depicted.

Parallel Resistors 100

Referencing the table above we see that parallel resistors’ equivalent resistance value is calculated using the reciprocal of reciprocal equation form, like this:

$latex X_{total} = \frac{1}{\frac{1}{100\Omega }+\frac{1}{100\Omega }+\frac{1}{100\Omega }}&s=2&bg=e5e6db$

$latex X_{total} = \frac{1}{\frac{3}{100}} &s=2&bg=e5e6db$   (…or otherwise as 1 / 0.03)

$latex X_{total} = 33.3\Omega &s=2&bg=e5e6db$

Equivalent Resistance

From an intuitive standpoint, perhaps considering a ‘water flowing in pipes’ analogy to the circuit depiction above, this makes sense.  In the parallel arrangement the total resistance to current flow offered by three equivalently sized pipes will be less than the resistance of any single pipe of the same size.

series resistors-a

Three resistors in a series connection arrangement would use the Sum of Components equation form.

If the three resistors were instead arranged in series, one behind the other and each offering additional resistance to the current flow in a single loop, the resistor values would add in accordance with the Sum of Components equation form above.  [In the series arrangement scenario, total resistance would be 100+100+100 = 300 ohms.]

You can practice the application of the Sum of Components and the Reciprocal of Reciprocal equation forms with the section 6.3 quiz under the Learning Material menu, General Book Section Media submenu item.

The answer to General Class question G5C04, What is the total resistance of three 100-ohm resistors in parallel? is “C. 33.3 ohms.”

Related Questions:  G5B02, G5C03, G5C05, G5C08 through G5C15