Question

I need help and a bit confused on the following questions. Thanks in advance!

1. Three resistors with resistances of 5.0 ?, 9.0 ?, and 12.0 ?, respectively, are connected in a series circuit with a 6.0 V battery. Find the potential difference across the 5.0 ? resistor.

2. Following the steps and answering the questions below, find the equivalent resistance of the combination of resistors shown in the figure:

We will break this complex circuit into simpler combinations of resistors in series or parallel.

A. Identify the two resistors that are in a simple series combination. List them:

i. Lowest: _________

ii. Highest: _________

B. What is the equivalent resistance of the two resistances you listed in part a.?

C. Identify the two resistors that are in a simple parallel combination. List them:

i. Lowest: _________

ii. Highest: _________

D. What is the equivalent resistance of the two resistances you listed in part c.?

We can now replace the two series and two parallel resistances with their equivalent resistances and draw a simpler circuit, as shown above.

e. What is the equivalent resistance of the 8.00 ?? and Rs1 resistors?

We can reduce the diagram even further, as shown below.

f. What is the equivalent resistance of the 1.50 ?? and Rp1 resistors?

Finally, we have reduced the circuit to just two resistors.

g. What is the equivalent resistance of the two resistors, Rp2 and Rs2, above?

Answer 1

1) R equivalent = 5 + 9 + 12 = 26 ohms

V = I R

I = V/R = 6/26

V 5 ohm = I R = 6*5/26 = 30/26 = 1.15 V

2)

A) i. 3.18 ii. 3.5

b) 3.18 + 3.5 = 6.68 uohms

c. i 0.75 ii 10.2

d) 1/0.75 + 1/10.2 = 1/R

R=0.699 u ohms

e) 1/8 + 1/6.68 = 1/R

R=3.64 uohms

f) 1.5 + 0.699 = 2.20 uohms

g) 1/2.2 + 1/3.64 = 1/R

R=1.37 uohms

Answer 2

1.

equivalent resistance

R_eq=5+9+12 =26 ohms

Total current flowing in the circuit

I=V/R_eq=6/26=0.23 A

Potential difference across 5 ohms

V₅=0.23*5=1.15 Volts

2.

a)

Lowest :3.18 uohms

Highest:3.5 uohms

b)

R_s1=3.18+3.5 =6.68 iohms

c)

Lowest :0.75 uohms

Highest:10.2 uohms

d)

1/R_p1=1/0.75 +1/10.2

R_p1=0.6986 uohms

e)

1/R_p2=1/6.68 +1/8

R_p2=3.64 uohms

f)

R_s2=1.5+0.6986=2.1986 uohms

g)

1/R_eq=1/2.1986 +1/3.64

R_eq=1.37 uohms