Application of Differentiation and Integration in Circuit Analysis Problem

Application of Differentiation and Integration in Circuit Analysis Problem

1. What is differentiation?

   • It is concerned with the rate of change of one quantity relative to another. If the quantity continue changing( velocity, acceleration and current in a circuit), we can use differentiation study the nature of their changes.
     • 1. First Principle 2. Chain Rule 3. Product Rule, Quotient Rule and Power Rule 4  Implicit and parametric equations 5. Exponential, logarithmic and trigonometric function 6. Standard function

2. What is Integration?

   • A branch of calculus which involved the reverse process of differentiation.
     • Evaluate Integrals method 1. Integration by parts 2. Partial Fraction 3. Substitutions

3. Question

   • Find the Rate of Current at Time, t=0
     • Calculation
     • The above RL circuit is connected across a constant voltage source, and a switch, S is open until it closed at a time t=0, and remains permenantly closed producing a "step response" type voltage input. The current, i begins to flow through the circuit but does not rise rapidly to its maximum value of Imax as determined by the ratio of V/R (Ohms Law)

4. conclusion

   • RL Circuit can be combine with the RC Circuit in order to form RLC circuit (which consists of a resistor, inductor, capacitor in series or in parallel) to perform as variable tuned circuit, filters, oscillators, voltage multiplier and pulse discharge circuit. These are also widely used in electronic filter.

5. Problem Statement

   • How differentiation and integration method can be apply in RL Circuit

6. Objective

   • 1.To understand the derivation of current in RL circuit
   • 2. To enhance student in creating mind map for understanding mathematic consept and solving problem

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