TP 21.41

Given: R₁ = 1.50 W

R₂ = 2.50 W

R₃ = 4.80 W

R₄ = 3.30 W

R₅ = 8.10 W

R₆ = 6.30 W

DV = 9.00 V

(a) Find: I₁, I₂, I₃, I₄, I₅, I₆

From TP 21.37:

1/R₃₄₅ = 1/R₃ + 1/R₄ + 1/R₅ = 1/(4.80 W) + 1/(3.30 W) + 1/(8.10 W) = 0.634 W^-1 R₃₄₅ = 1.58 W

R₃₄₅₆ = R₃₄₅ + R₆ = 1.58 W + 6.30 W = 7.88 W

1/R₁₂₄₅₆ = 1/R₁ + 1/R₂ + 1/R₃₄₅₆ = 1/(1.50 W) + 1/(2.50 W) + 1/(7.88 W) = 1.19 W^-1 R₁₂₃₄₅₆ = 0.838 W

Let’s start with resistor R₁:

DV₁ = I₁ R₁

I₁ = DV₁/ R₁ = (9.00 V)/(1.50 W) = 6.00 A

For resistor R₂:

DV₂ = I₂ R₂

I₂ = DV₂/ R₂ = (9.00 V)/(2.50 W) = 3.60 A

For the combination of resistors R₃, R₄, R₅, and R₆:

DV₃₄₅₆ = I₃₄₅₆ R₃₄₅₆

I₃₄₅₆ = DV₃₄₅₆/ R₃₄₅₆ = (9.00 V)/(7.88 W) = 1.14 A

Notice: it is a series combination of R₃₄₅ and R₆:

I₆ = I₃₄₅₆ = 1.14 A

also, DV₆ = I₆ R₆ = (1.14 A) (6.30 W) = 7.20 V

DV₃ = DV₄ = DV₅ = 9.00 V - 7.20 V = 1.80 V

For resistor R₃:

DV₃ = I₃ R₃

I₃ = DV₃/ R₃ = (1.80 V)/(4.80 W) = 0.375 A

For resistor R₄:

DV₄ = I₄ R₄

I₄ = DV₄/ R₄ = (1.80 V)/(3.30 W) = 0.545 A

For resistor R₅:

DV₅ = I₅ R₅

I₅ = DV₅/ R₅ = (1.80 V)/(8.10 W) = 0.222 A

(b) Less, see (a)