Question

A 2.00-µF and a 7.70-µF capacitor can be connected in series or parallel, as can a 21.0-kΩ and a 100-kΩ resistor. Calculate the four RC time constants possible from connecting the resulting capacitance and resistance in series.

(a) resistors and capacitors in series
s

(b) resistors in series, capacitors in parallel
s

(c) resistors in parallel, capacitors in series
s

(d) capacitors and resistors in parallel
s

Answer 1

(a)

Series combination of resistors is given as

R = 21.0 + 100

R = 121 kohm

R = 121000 ohm

Series combination of capacitors is given as

C = Product of capacitors/(Sum)

C = (2.00)(7.70)/(2.00 + 7.70)

C = 1.6 F

C = 1.6 x 10^-6 F

Time constant is given as

T = RC

T = (121000) (1.6 x 10^-6)

T = 0.194 sec

b)

Series combination of resistors is given as

R = 21.0 + 100

R = 121 kohm

R = 121000 ohm

Parallel combination of capacitors is given as

C = 2.00 + 7.70 = 9.70 F = 9.70 x 10^-6 F

Time constant is given as

T = RC

T = (121000) (9.70 x 10^-6)

T = 1.2 sec

C)

Parallel combination of resistors is given as

R = Product of resistors/(Sum)

R = (21.0) (100)/(21.0 + 100)

R = 17.4 ohm

Series combination of capacitors is given as

C = Product of capacitors/(Sum)

C = (2.00)(7.70)/(2.00 + 7.70)

C = 1.6 F

C = 1.6 x 10^-6 F

Time constant is given as

T = RC

T = (17.4) (1.60 x 10^-6)

T = 27.8 x 10^-6 sec

D)

Parallel combination of resistors is given as

R = Product of resistors/(Sum)

R = (21.0) (100)/(21.0 + 100)

R = 17.4 ohm

Parallel combination of capacitors is given as

C = 2.00 + 7.70 = 9.70 F = 9.70 x 10^-6 F

Time constant is given as

T = RC

T = (17.40) (9.70 x 10^-6)

T = 168.8 x 10^-6 sec