Calculate the current through each resistor in (Figure 1) if each resistance R =

Question

Calculate the current through each resistor in (Figure 1) if each resistance R = 2.25 k and V = 16.0 V .

Part A Calculate the current through resistor a. Express your answer to three significant figures and include the appropriate units. Ia =

Part B Calculate the current through resistor b. Express your answer to three significant figures and include the appropriate units. Ib =

Part C Calculate the current through resistor c. Express your answer to three significant figures and include the appropriate units. Ic =

Part D Calculate the current through resistor d. Express your answer to three significant figures and include the appropriate units. Id =

Part E Calculate the current through resistor e. Express your answer to three significant figures and include the appropriate units. Ie =

Part F Calculate the current through resistor f. Express your answer to three significant figures and include the appropriate units. If =

Part G What is the potential difference between points A and B? Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

Here ,

R = 2.25 kOhm

V = 16 V

for a and b in series

R1 = R + R = 2 R

for c and R1 in parallel

1/R2 = 1/(2R) + 1/R

R2 = 0.667 R

for R2 and d in series

R3 = 0.667 R + R

R3 = 1.667 R

for e and R3 in parallel

1/R4 = 1/(1.667 * R) + 1/R

R4 = 0.625 * R

R4 and f in series

R5 = 0.625 * R + R

R5 = 1.625 * R

R5 = 2.25 * 1.625 kOhm

R5 = 3.66 kOhm

part a)

now , current through f , If = V/R5

If = 16/(3.66) mA

If = 4.38 mA

current in resistance d ,Using current divider

Id = e * If/(e + R3)

Id = 3.66 * R/(R + 1.667 * R)

Id = 1.37 mA

Now , for the current through a

Using current divider rule

Ia = Id * R/(R + R1)

Ia = 1.37 * 1/(1 + 2)

Ia= 0.46 mA

the current in resistance a is 0.46 mA

b)

as current in a = current in b

current in resistance b is 0.46 mA

c)

current in resistance c = current in d - current in a

current in resistance c = 1.37 - 0.46

current in resistance c = 0.903 mA

the current in resistance c is 0.903 mA

d)

current in the resistance d = Id

current in the resistance d = 1.37 mA

e)

current in resistance e = current in f - current in d

current in resistance e = 4.38 mA - 1.37 mA

current in resistance e = 3.01 mA

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