In the figure below, Ri-10.0 ?, R2-R3-4.0 ?, R,-20.0 ?, and the ideal battery ha

Question

In the figure below, Ri-10.0 ?, R2-R3-4.0 ?, R,-20.0 ?, and the ideal battery has emf 6.00 V (a) (2 Pts.) What is the equivalent resistance of the whole circuit? (b) (2 Pts.) What is i in resistance 1? (c) (2 Pts.) What is the potential at junctions A? and B? (d) (2 Pts.) What is i in resistance 2 and 3? (e) (2 Pts.) What is i in resistance 4? 1. Ri Ri 2. (5 Pts.) In the figure below, &1-9.0V, &-6.0 V, and -2.02. Write down the "Loop Rule" for the circuit and use that to answer: What value must R have if the current in the circuit is to be 80 mA? 18

Explanation / Answer

here,

1)

R2, R3 and R4 in parallel, let their equivalent be R5

1/R5 = 1/R1 + 1/R2 + 1/R3

1/R5 = 1/4 + 1/4 + 1/20

solving for R5

R5 = 1.82 ohm

EMF = 6 V

a)

the equivalent resistance , Req = R5 + R1 = 11.8 ohm

b)

the i in R1 , I1 = EMF /Req = 0.51 A

c)

the potential difference at A and B , V = EMF - I1 * R1

V = 0.92 V

d)

the current in 2 and 3 , I2 = V/R2 = 0.23 A

e)

the current in 4 , I4 = V/ R4 = 0.046 A

2)

using KVL

E1 - E2 = I * ( R + r1 + r2)

9 - 6 = 0.08 * ( R + 2 + 2)

solving for R

R = 33.5 ohm

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