Question

Pre-Laboratory Work 3 (estimated time 1 hour) In reality, when a circuit is first connected to a power source the current through the circuit does not jump discontinuously from zero to its maximum value. Instead, the current increases smoothly due to the effect known as self-induction. The circuit itself can be seen as a current loop and as the current increases with time, the magnetic fields circling the wires become stronger. Thus, the magnetic flux through the loop itself increases, which induces a current in the opposite direction to that generated by the power source. This is known as back emf. As a result, the current through a circuit never changes discontinuously, but changes progressively over a time-scale set by the inductance of the loop. The self-induced emf is proportional to the rate of change of the current as dl EL-L- dt where L is the inductance of the loop. The SI unit of inductance is the henry (H), which is 1 H 1V s/A In this experiment you will study the effects of inductance on a circuit. Problem 1. Consider the RLC circuit below R a. Apply Kirchhoff's loop rule to this circuit and write the differential equation for the charge across this circuit. Project II- Circuits PHYS2080 Page 35

Answer 1

- E 0 using kischoff's loop rule. E = IR + x2 + Xc E = R de + dela + 8 solution for differential equation q=& max é 22 63 (Wot +O) © À 24t) d voltage acron resistor is VR = 3R V = Rde