Current, Voltage, and Power

Voltage is related to potential-energy difference. The voltage drop across any circuit element is directly proportional to the change in energy of a charge as it traverses the circuit element. Specifically, 1 volt = 1 joule/coulomb. The potential energy (with respect to some reference point) is equal to the voltage multiplied by the charge.

Current refers to the motion of charges. The current through a given surface (e.g. the cross-section of a wire) is defined as the net charge passing through that surface per unit time. The unit for current is the ampere: 1 ampere = 1 coulomb/second.

The product of voltage and current has units of joules/second, otherwise known as watts.

If the voltage drop across a circuit element equals the change in potential energy per unit charge, and the current equals the amount of charge moving through the element per unit time, then their product equals the power released within the device!
 
The power dissipated within any device is given by
P = IV (2.11)

For resistive elements (or when an effective resistance can be defined), Eq. 2.11 can be combined with Ohm’s law to give:
P = IV = I 2 R = V 2 /R  (2.12)

Resistors, diodes, transistors, relays, integrated-circuit chips, etc., are rated (in part) by their maximum allowed power. Exceeding these ratings can have  disastrous effects on your circuit, and may even cause a fire! To illustrate this point, our first exercise will deliberately lead to the destruction of a carbon-film resistor.

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Device Electrical Characteristics

The resistor is a linear device and is characterized by a “straight-line equation”. It dissipates power as heat, its value in ohms can vary as to the tolerance rating (ohms ± % of rated value). The resistor cannot store energy.

An inductor or capacitor is an energy storage device; a capacitor’s current or an inductor’s voltage does not change instantaneously. Initial conditions can apply to both of these devices.

The ideal capacitor has zero conductance or infinite resistance and the ideal inductor has zero resistance or infinite conductance. Ideally, neither device dissipates heat (power). The total power consumed or delivered in an RLC is presented as a complex variable (phasor) with a real (dissipated power by resistors) and imaginary (reactive power ) component.

It should be mentioned that, a capacitor’s conductance (or an inductor’s resistance) only approaches zero and the rated component value (Farads for capacitors or Henries for inductors) may also vary. These variants in addition to EMI and environmental effects would require you to alter your design or analysis somewhat, depending on how critical they are to your design or model.

The Ideal voltage vs. current characteristics for the resistor, inductor and capacitor are shown below in Table 1.

source : PDHengineer.com
Course No E-6002
First Order RLC Circuits: Time Domain
Analysis

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Kirchhoff’s Law

In 1845, German physicist Gustav Kirchhoff first described two laws that became central to electrical engineering. The laws were generalized from the work of Georg Ohm. The laws can also be derived from Maxwell’s equations, but were developed prior to Maxwell’s work. 

• Kirchhoff’s Current Law (KCL):

        The algebraic sum of  the currents entering any node is zero  

        This law is also called Node analysis

       This Law is used in circuit analysis to define relationships between currents flowing in branches of the circuit. For example, in figure above the currents flowing in the four branches connected to the node have been defined as I1, I2, I3, I4 and Kirchhoff’s Current Law allows us to write down an equation relating these currents. Looking closely at figure above, we see that two of the currents (I2, I3) are flowing towards the node, while the other two currents (I1, I4) are flowing outwards. The ‘algebraic sum’ needs to take account of this difference in relative direction.

To apply Kirchhoff’s Current Law rigorously, we must first make an arbitrary choice of positive current direction. Suppose currents flowing in to the node (I2, I3) are treated as positive contributions to the algebraic sum (and conversely currents flowing from the node are treated as negative contributions), then the algebraic sum of currents would be written: - I1 + I2 + I3 - I4 , and according to Kirchhoff’s Current Law this algebraic sum is equal to zero:

                - I1 + I2 + I3 - I4 = 0

• Kirchhoff’s Voltage Law (KVL):

        The algebraic sum of  all voltages taken around a closed loop in a circuit is zero.
         This law is also called Loop analysis

The figure shows a circuit loop, which is part of a larger circuit. The loop involves four nodes, ABCD, between which are connected four components. We must recognise that the direction of voltages matters when using Kirchhoff’s Voltage Law.

In this case the four components are resistances, but Kirchhoff’s Voltage Law can be applied no matter what components are connected in the closed circuit loop. The voltages across the four resistances comprising the circuit loop have been defined as V1, V2, V3,V4 and Kirchhoff’s Voltage Law allows us to write down an equationrelating these voltages. 

If we think about travelling around the closed circuit loop in any direction, we note that the four voltages will be encountered in sequence. Two of the voltage arrows will point in the direction of travel and two will oppose the travel. The ‘algebraic sum’ of voltages needs to take account of this difference in relative direction.

To apply Kirchhoff’s Voltage Law correctly, we must make arbitrary choices about the direction of travel around the closed circuit loop and the contribution which the separate voltages make to the algebraic sum around the closed circuit loop. Suppose we travel around the loop in Fig. 2.2 in the clockwise direction (ABCD) and that voltages opposite to the direction of travel make a positive contribution to the algebraic sum. In travelling from A to B the voltage V1 is encountered and it is in a direction which is opposite to the travel. Therefore, V1 is a positive contribution to the algebraic sum. The same comment is true of V2, which is met when proceeding from B to C. However, travelling from C to D and back to A, the voltages V3 and V4 are encountered and in both cases the voltages are in the same direction as the travel, giving a negative contribution to the algebraic sum. 

Expressed mathematically, the algebraic sum of voltages around the closed loop ABCD is: 

            + V1 + V2 - V3 - V4 

and Kirchhoff’s Voltage Law states that this sum is equal to zero:
           + V1 + V2 - V3 - V4 = 0

Recall the Ohm Law that V = IR

 

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OHM’S LAW

An excellent analogy for the simplest of electrical circuits is the water in a hose connected to a pressure valve. Think of the electrons in the copper wire as the water in the hose, the pressure valve as the applied voltage, and the size of the hose as the factor that determines the resistance. If the pressure valve is closed, the water simply sits in the hose without motion, much like the electrons in a conductor without an applied voltage. When we open the pressure valve, water will flow through the hose much like the electrons in a copper wire when the
voltage is applied. 

Current is a reaction to the applied voltage and not the factor that gets the system in motion. The more the rate of water flow through the hose, just as applying a higher voltage to the same circuit will result in a higher current. Ohm’s law in honor of Georg Simon Ohm, clearly reveals that for a fixed resistance, the greater
the voltage (or pressure) across a resistor, the more the current, and the more the resistance for the same voltage, the less the current. In other words, the current is proportional to the applied voltage and inversely proportional to the resistance.

The current I of Eq. results from applying a dc supply of E volts across a network having a resistance R ohm.

Taken from : Introductory Circuit Analysis 10th Edition by Boylestad

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