Solved Examples
Find peak current flowing through an inductor having an inductance of 100 mH connected with a voltage pulse generator having amplitude of 5 V and pulse width of 0.1 ms.
[Tex]I = \frac{1}{L}\int_{0}^{T}Vdt\\ \hspace{1mm}\\ I = \frac{1}{100\times10^{-3}}\int_{0}^{0.1\times{10^{-3}}}5dt\\ \hspace{1mm}\\ I = \frac{1}{10^{-1}}\int_{0}^{10^{-4}}5dt\\ \hspace{1mm}\\ I = 10[5t]_{0}^{10^{-4}}\\ \hspace{1mm}\\ I = 10[(5\times{10^{-4}})-(5\times0)]\\ \hspace{1mm}\\ I = 5\times{10^{-3}}\\[/Tex]
∴ I = 5 mA
Find the inductance of an inductor connected with constant voltage source of 12 V switched at t = 0 for 1 ms. The peak current flowing through the circuit is 100 mA.
[Tex]I = \frac{1}{L}\int_{0}^{T}Vdt\\ \hspace{1mm}\\ L = \frac{1}{100\times10^{-3}}\int_{0}^{10^{-3}}12dt\\ \hspace{1mm}\\ L = \frac{1}{10^{-1}}\int_{0}^{10^{-3}}12dt\\ \hspace{1mm}\\ L = 10[12t]_{0}^{10^{-3}}\\ \hspace{1mm}\\ L = 10[(12\times{10^{-3}})-(12\times0)]\\ \hspace{1mm}\\ L = 12\times{10^{-2}}\\[/Tex]
∴ L = 120 mH
Find the voltage across the load resistor of 10 kΩ connected across an inductor having inductance of 15 mH. The entire circuit is powered by a voltage pulse generator which generates 9 V pulses having a pulse width of 2 μs.
[Tex]I = \frac{1}{L}\int_{0}^{T}Vdt\\ \hspace{1mm}\\ I = \frac{1}{15\times10^{-3}}\int_{0}^{2\times{10^{-6}}}9dt\\ \hspace{1mm}\\ I = \frac{10^3}{15}\int_{0}^{2\times{10^{-6}}}9dt\\ \hspace{1mm}\\ I = 66.67[9t]_{0}^{2\times{10^{-6}}}\\ \hspace{1mm}\\ I = 66.67[(9\times2\times{10^{-6}})-(9\times0)]\\ \hspace{1mm}\\ I = 1.2\times{10^{-3}}\\ \hspace{1mm}\\ V = IR\\ \hspace{1mm}\\ V = 1.2\times10^{-3}\times10000\\[/Tex]
∴ V = 12 V
Inductor I-V Equation in Action
The inductor is a passive element that is used in electronic circuits to store energy in the form of magnetic fields. It is usually a thin wire coiled up of several turns around a ferromagnetic material. Inductors are used in transformers, oscillators, filters, etc. The amount of energy that can be stored by the inductor in the form of the magnetic field is called inductance measured in Henry named after the famous scientist Joseph Henry.
Inductor works on the principle of one of Maxwell’s four equations which states that a changing electric field produces a changing magnetic field and vice versa. Unlike a capacitor, an inductor cannot sustain the stored energy as soon as the external power supply is disconnected because the magnetic field decreases steadily as it is responsible for current flow in that circuit in the absence of the power supply.
Table of Content
- Inductor I-V Equations
- Relation Between Current and Voltage
- Inductor Voltage is Proportional To The Rate of Change of Current
- Inductor and Current Source
- Inductor and Voltage source
- Inductor and Switch
- Solved Examples