Circuit analysis: Six resistors and two batteries

In summary, the conversation discusses the construction of a circuit with six resistors and two ideal batteries. It also includes finding the currents, the power dissipated in each resistor, the power delivered to or by each battery, and the total power dissipated and delivered. Equations are provided for calculating the currents and power dissipation.
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littlejay21
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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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  • #2
It's going to be hard to do anything with your post considering that it's just a bunch of numbers and equations that have no relevance to anything (since you did not attach a circuit diagram) without even a question about any of it.
 
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Likes berkeman and kuruman

FAQ: Circuit analysis: Six resistors and two batteries

1. How do you calculate the total resistance in a circuit with six resistors and two batteries?

To calculate the total resistance in a circuit with six resistors and two batteries, you can use the formula R = R1 + R2 + R3 + R4 + R5 + R6, where R1-R6 represent the individual resistances of each resistor. You can also use the parallel and series combination formulas to simplify the calculation.

2. What is the difference between series and parallel circuits?

In a series circuit, the components are connected one after another, so that the current flows through each component in order. In a parallel circuit, the components are connected side by side, so that the current can flow through each component simultaneously. This results in different calculations for total resistance and current in each type of circuit.

3. How do you determine the current flowing through each resistor in a circuit?

To determine the current flowing through each resistor in a circuit, you can use Ohm's Law (I = V/R) and Kirchhoff's Current Law, which states that the total current entering a junction is equal to the total current leaving the junction. By applying these principles and using the appropriate formulas, you can solve for the current in each resistor.

4. What is the purpose of using two batteries in a circuit?

Two batteries can be used in a circuit to increase the voltage, which can be useful when powering devices that require a higher voltage than a single battery can provide. The batteries can be connected in series to add their voltages together, or in parallel to increase the current capacity.

5. How can you troubleshoot a circuit with six resistors and two batteries that is not functioning properly?

To troubleshoot a circuit, you can use a multimeter to measure the voltage and current at various points in the circuit. This can help you identify any faulty components or connections. You can also use circuit analysis techniques, such as Kirchhoff's Laws and Ohm's Law, to check the calculations and make sure the circuit is properly designed and connected. If necessary, you can also use circuit simulators to simulate the circuit and identify potential issues.

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