(PLEASE answer letter c part i and ii) Three resistors are connected in the circ

Question

(PLEASE answer letter c part i and ii) Three resistors are connected in the circuit shown below. The emf of the battery is 18.0 V and the resistors have the following values: R1 = cR, and R2 = R/c, where R = 20.0 and c is a positive number between 0 and infinity. R3 is an unknown constant value.

(a) As the value of c approaches zero, the current through the battery approaches 0.257 A. What is the resistance of R3?
70.0389
(b) What does the value of the current through the battery approach as c approaches infinity?

zero

(c) If the value of c is set to 3.10, determine the following.

(i) The equivalent resistance of the circuit

(ii) The current through R2

Explanation / Answer

a) net resistance of the ckt,

Rnet = R1 + 1/(1/R2 + 1/R3)

= c*R + 1/(1/(R/c) + 1/R3)

= c*R + 1/(c/R + 1/R3)

AS c approches zero,

Rnet = R3

use, I = V/Rnet

Rnet = V/I

R3 = V/I

= 18/0.257

= 70.0389 ohms

b) Rnet = R1 + 1/(1/R2 + 1/R3)

= c*R + 1/(1/(R/c) + 1/R3)

As c approches infinite,

Rnet = infinite

so, I = 0

c) Rnet = R1 + 1/(1/R2 + 1/R3)

= 3.1*20 + 1/(1/(20/3.1) + 1/70.0389)

= 67.907 ohms

d) I1 = V/Rnet

= 18/67.907

= 0.265 A

voltage across R2, V2 = V - V1

= V - I1*R1

= V - I1*c*R

= 18 - 0.265*3.1*20

= 1.57 volts

I2 = V2/R2

= V2/(R/c)

= c*V2/R

= 3.1*1.57/20

= 0.24335 A

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