Question

A series RL circuit with L = 3.00 H and a series RC circuit with C = 3.00 F have equal time constants. If the two circuits contain the same resistances R, (a) what is the value of R and (b) what sit the time constant?

Answer 1

A series RL circuit with inductance L = 3.00 H series with RC circuit

capacitance C = 3.00 F

   resistance is R

a ) time constant for RC circuit is τ = RC  ........(1)

time constant for RL circuit is τ = L / R ........(2)

from the above two R^2 = L / C

                                 R = √ L/ C

                                       = √ 3.00 H / 3.00 F

                                        = 1 Ω

b ) time constant is τ = RC

                                     = 1.00Ω * 3.00 F

                                     = 3.00 s