Example 6-13: Find and sketch v₁(t) and i, (t) for the circuit below. t=0 v₁(t) V₂(t) + WW R3 1. ↑ R₁ 1 ΚΩ 1 ΚΩ 1 ΚΩ L 5
Posted: Thu May 05, 2022 3:06 pm
- 1 (257.31 KiB) Viewed 24 times
- 2 (215.18 KiB) Viewed 24 times
I understood the first page, but I want to ask the highlighted part.
My question:
Why (R1||R2)+R3 but not R1 || R2 ||R3 in first highlighted equation?
If inductor behaves as short circuit, it seems like all resistors are in parallel.
The calculation for time constant also has the same problem.
Example 6-13: Find and sketch v₁(t) and i, (t) for the circuit below. t=0 v₁(t) V₂(t) + WW R3 1. ↑ R₁ 1 ΚΩ 1 ΚΩ 1 ΚΩ L 50 μH 1 mA Soln.: Prior to switching, v₁(0-) = I₂R₁ = 1 V ie (0-) = 0 A (and v₂(0-) = 0 V) At the instant of switching, with continuity of the inductor current, and i, (0+) = i,(0-) = 0 A i,(0+) 1 v₁ (0+) = I,(R₁||R₂) = 1mx500 = 0.5 V For more complicated RC and RL circuits, the time constant is given by t=RegC or L/Rear where Reg is the equivalent resistance as seen by the capacitor or inductor. 6-18 WW S₁ R₂
At t-00, L behaves as a short circuit, and i, (∞0) = Is(R₁||R₂)/((R₁||R₂)+R3) = 1mx0.5k/1.5k = 0.333 MA v₁(00) = Is(R₁||R₂||R3) = 1mx333 = 0.333 V Use equivalent resistance to compute the time constant: = L/((R₂₁||R₂) +R3) T = 33.3 ns WWW R₁||R₂ 1, R₁ R₂ = (1) + Is(R₁||R₂) F 1 V 0.5 V 0 0.5 mA- 0 I v₁ (t) 0.33 V 50n 100n150n 0.33 mA ię (t) 50n 100n 150n t/s →t/s