Question

Please fully explain

8) Consider three resistors: R1-6 Ω, R2-12 Ω, R3-21 Ω a) Connect the three resistors in a circuit (make a circuit drawing) such that the effective resistance is the smallest it can be: b) Are the three resistors above connected in series, parallel, or some other combination? parallel. c) What is the effective resistance of this circuit that has the smallest effective resistance using these three resistors? 3.36 S2 d) Connect all three resistors in a circuit (make a circuit drawing) such that the effective resistance is between 6 and 12 ohms. If no combination will work, then write NONE.

Answer 1

When resistors are connected in parallel combination equivalent resistance is smaller than the resistance of individual resistors. Rightdoublearrow In parallel combination 1/R_eq = 1/R_1 + 1/R_2 + 1/R_3 1/R_eq = 1/6 omega + 1/12 omega + 1/21 omega R_eq = 3.36 omega it is less than all three resistance 6 omega, 12 omega and 21 omega \r\n Part d Desired equivalent resistance 6 omega < R_eq < 12 omega Since equivalent resistance is greater than 6 omega, it should be connected in series. It is also less than 12 omega and 21 omega, They should be in parallel. Let's try to find equivalent resistance of following circuit 12 omega and 21 omega are in parallel 1/R^23_eq = 1/R_2 + 1/R_3 = 1/12 omega + 1/21 omega R^23_eq = 7.6 omega Then reduced circuit \r\n equivalent resistance R_eq = 6 omega + R_eq^2 R_eq = 6 omega + 7.63 omega R_eq = 13.6 omega