### 1. In this Chapter

We begin this chapter by exploring a couple of the basic rules of circuit analysis: Ohm’s Law and Power Law then apply them to a simple RC circuit and calculate the current, voltage, and power dissipation. We will use the NI Multisim circuit teaching environment to verify our calculated results with example circuits that can be used by any educator or student.

If you do not have NI Multisim installed on your computer, you can download a free 30 day evaluation at http://www.ni.com/multisim/try/

### 2. Example Courses

Listed below are example courses that teach this concept at their schools.

Course Name | School | Learn More |

Electrical Principles | Conestoga College | http://www.conestogac.on.ca/fulltime/0071.jsp |

Electronic Technology 1 | Macomb Community College | http://www.macomb.edu/noncms/Search/Courses/coursekey.asp?coursekey=ELEC-1161) |

### 3. Ohm’s Law

Ohm’s Law states that the voltage drop across a device is directly proportional to the current passing through it. The constant of proportionality is its resistance.

**V = I x R **[1]

### 4. Power Law

The Power Law states that the power dissipated in a device is inversely proportional to the squared value of the voltage across it:

**P = V ^{2}/R **[2]

It can also be stated as the power dissipated in a device is directly proportional to the squared value of the current going through it:

**P = I ^{2} x R **[2]

Also, the power law can be dictated simply as:

**P = V x I **[2]

### 5. Example Problem

Let us now examine the below circuit and apply the above laws to determine the different currents and voltages as well as the power dissipated.

__STEP 1:__ Open circuit file “rc_circuit.ms12” using NI Multisim. You will see the circuit below [3].

__Answer Sub-Step 1: Consider the “Immediately after closing switch” phase__

Assume the capacitors are completely uncharged.

__Immediately after__ we close the switch, the capacitors will remain uncharged (since they do not charge instantaneously) and therefore the voltage drop across them will be equal to zero; i.e. current will pass through them freely as in a simple wire. [3, 4]

__STEP 2:__ Open Circuit file “rc_after_closing.ms12” which shows the following circuit:

Since there is a short circuit, the current will not pass through the **R _{1}** and

**R**branches.

_{3}__Answer Sub-Step 2: Calculate the voltage drop in the above circuit__

Using Ohm’s Law: __lculate the power dissipated in the above circuit__

Using the Power Law in **R _{2}** :

**P = I**= 3

^{2}x R^{2}x 4 =

**36W**

__Answer Sub-Step 4: Consider the “Steady State” phase of the above circuit__

In this case the above circuit representation is no longer valid. The capacitors when fully charged will not allow any more current to go through and therefore will act as open circuits, and all the resistors __in series__ will those capacitors will then behave as simple wires. [3, 4]

__STEP 3:__ Open circuit file “rc_steady_state.ms12”. You will notice the following circuit:

__Answer Sub-Step 5: Calculate the voltage drop for the above circuit__

Since no current is passing through the capacitor C1, we will consider the left loop only and can calculate:

**R _{series}** =

**R**+

_{1}**R**=

_{2}**6 Ω**

Therefore: **V = I x R** and **I** = 12 / 6 = **2 A**

__Answer Sub-Step 6: Calculate the power dissipated in the above circuit__

The power dissipated in the **R _{1}** :

**P = I**= 2

^{2}x R^{2}x 2 =

**8 W**

And for **R _{2}** :

**P = 16W**

__STEP 4:__ Re-open circuit file “rc_after_closing.ms12” then double-click on the multimeter to open the front panel and choose the “A” button to measure the current. Then, simulate the circuit by clicking on the run button or choosing “Simulation>>Run Simulation”.

You will notice that the current passing through the circuit is indeed 3 A which confirms the correct value of the calculated power as well.

__STEP 5:__ Re-open circuit file “rc_steady_state.ms12” then again double-click on the multimeter to open the front panel and choose the “A” button to measure the current. Then, simulate the circuit by clicking on the run button or choosing “Simulation>>Run Simulation”.

Thus we have verified that the calculated current value is correct and therefore the power dissipated across the two resistors is also correct.

### 6. Suggested NI Solution

National Instruments offers a number of products that combine to provide a scalable and powerful teaching platform for educators. The solution includes:

NI Multisim circuit teaching environment: Combining an intuitive circuit definition environment, with powerful SPICE simulation technology, educators can use NI Multisim to easily teach the ins-and-outs of circuits in a safe environment.

NI ELVIS teaching and measurement platform allows educators to provide students with a compact, all-in-one unit for their measurement and analysis needs. Combining an oscilloscope, function generator, DMM, bode analyzer and 8 other instruments into a small platform; it simplifies the laboratory experience for students and lab instructors.

### 7. References

[1] Hoppe, Patrick. Wisconsin Technical College System. “Wisc-Online”. __Ohm’s Law: The Relationship of Voltage, Resistance, and Current.__

[http://www.wisc-online.com/Objects/ViewObject.aspx?ID=DCE8104]. (05/02/2013)

[2] Georgia State University, Department of Physics and Astrology. “DC Circuits”. __DC Electric Power.__

[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elepow.html#c1]. (05/02/2013)

[3] Brightstorm. “RC Circuits”. RC __Circuits.__

[http://www.brightstorm.com/science/physics/electricity/rc-circuits/]. (18/01/2013)

[4] W. G. Olgham, University of California. “RC Circuits”. __Charging and discharging in RC circuits.__

[http://www-inst.eecs.berkeley.edu/~ee42/sp01/LectNotes/Lect8.PDF]. (05/02/2013)