Write the clockwise mesh current equations for the following network using general approach. Redraw the network with proper current direction and voltage polarities through all the resistor and battery. Use E1=10V, E2=15V, E3=20V, E4=5V and R1=1kΩ, R2=2kΩ,R3=3kΩ, R4=4kΩ, R5=5kΩ Use the above values in the equation and simplify. Next solve the equations and find the value and direction of current through R3 resistor

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Thevenin Theorem

Any linear circuit, no matter how complex, maybe simplified to an equivalent circuit utilizing only a single voltage source and series resistance coupled to a load, according to Thevenin's Theorem. The superposition principle says that all foundational equations must be linear, and the notion of "linear" is still the same (i.e., there should not be any exponentials or roots). This is particularly the case when operating with passive elements like resistors, inductors, and capacitors. However, some components (particularly some gaseous and semiconductor devices like tunnel diode, Schottky diode, transistors like BJT, MOSFET) are nonlinear, meaning their current resistance fluctuates with voltage and current. As a result, circuits made up of these parts are known as nonlinear circuits.