# Circuit analysis: Six resistors and two batteries

## Homework Statement:

)
A circuit is constructed with six resistors and two ideal batteries as shown. The battery emfs are ε1 = 18 V and ε2 = 12 V. The values for the resistors are: R1 = R5 = 55 Ω, R2 = R6 = 110 Ω, R3 = 44 Ω, and R4 = 117 Ω. The chosen positive directions for the currents are indicated by the directions of the arrows.
Figure 1:
(a) Find all currents. Are the assumed current directions correct? (15pt)
(b) Find the power dissipated in each resistor. (3pt)
(c) Find the power delivered to or by each battery and indicate “delivered to” or “delivered
by” for each. Which battery (if any) is being charged? (1pt)
(d) Find the total power dissipated and the total power delivered. Are they the same? (1pt)

## Relevant Equations:

a) I4= I5 + I1
I2= I4 + I3
I5R1 - I4R2 - I3R45 + R6= 0
E1 + I1R3 - I4R2 - E2 + R6 = 0
E2-I3R45 = 0
I1= 0.2798 A
I2= 1.5720 A
I3= 0.06977 A
I4= 1.5022 A
I5= 1.2224 A

b) P=IV=IR^2
Problem Statement: )
A circuit is constructed with six resistors and two ideal batteries as shown. The battery emfs are ε1 = 18 V and ε2 = 12 V. The values for the resistors are: R1 = R5 = 55 Ω, R2 = R6 = 110 Ω, R3 = 44 Ω, and R4 = 117 Ω. The chosen positive directions for the currents are indicated by the directions of the arrows.
Figure 1:
(a) Find all currents. Are the assumed current directions correct? (15pt)
(b) Find the power dissipated in each resistor. (3pt)
(c) Find the power delivered to or by each battery and indicate “delivered to” or “delivered
by” for each. Which battery (if any) is being charged? (1pt)
(d) Find the total power dissipated and the total power delivered. Are they the same? (1pt)
Relevant Equations: a) I4= I5 + I1
I2= I4 + I3
I5R1 - I4R2 - I3R45 + R6= 0
E1 + I1R3 - I4R2 - E2 + R6 = 0
E2-I3R45 = 0
I1= 0.2798 A
I2= 1.5720 A
I3= 0.06977 A
I4= 1.5022 A
I5= 1.2224 A

b) P=IV=IR^2

N/A

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