Now it is a simple matter to find the current in each of the resistors.

  • Thread starter hobo skinoski
  • Start date
In summary: I1 = E/(R1234+R234)I've tried a bunch of different combos, and I'm just wondering if there is some sort of way to do this.As Gear300 suggests you should first find the equivalent resistance of the entire network because that will yield the current from the E source. Then it is simply a matter of splitting the current between the legs as you go through the network.The equivalent resistance R1234 is found by finding R23 = R2 + R3Then R234 = R4 || R23Then R1234 = R1 + R234Then I = E/R1234 or I1 = E
  • #1
hobo skinoski
2
0
Four resistors are connected to a battery as shown in the figure. The current in the battery is I, the battery emf is E, and the resistor values are R1 = R, R2 = 2R, R3 = 4R, and R4 = 3R.

p21-32.gif


-Determine the potential difference across each resistor in terms of E.
-Determine the current in each resistor in terms of I.
-In the limit that R3 → infinity, what are the new values of the current in each resistor in terms of I, the original current in the battery?


Homework Equations


V=IR
Rtotal=R1+R2+... (Series)
1/2Rtotal=1/R1 + 1/R2 ... (Parallel)


The Attempt at a Solution



I've tried a bunch of different combos, and I'm just wondering if there is some sort of way to do this.
 
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  • #2
hmm still trying. anyone out there?
 
  • #3
R2 and R3 are in series...we'll call their combination Rs. R4 is parallel to Rs...we'll call their combination Rp. R1 is in series with Rp...we'll call their combination Rt. Once you find Rt, the circuit should simply be a battery in series with a resistance of Rt. From this, you could find I1, the current running through the battery and R1. I1 splits into I2 and I3 at a junction. Note that the voltage between the junctions is the same per path.
 
  • #4
hobo skinoski said:
Four resistors are connected to a battery as shown in the figure. The current in the battery is I, the battery emf is E, and the resistor values are R1 = R, R2 = 2R, R3 = 4R, and R4 = 3R.-Determine the potential difference across each resistor in terms of E.
-Determine the current in each resistor in terms of I.
-In the limit that R3 → infinity, what are the new values of the current in each resistor in terms of I, the original current in the battery?


Homework Equations


V=IR
Rtotal=R1+R2+... (Series)
1/2Rtotal=1/R1 + 1/R2 ... (Parallel)

The Attempt at a Solution



I've tried a bunch of different combos, and I'm just wondering if there is some sort of way to do this.

As Gear300 suggests you should first find the equivalent resistance of the entire network because that will yield the current from the E source. Then it is simply a matter of splitting the current between the legs as you go through the network.

The equivalent resistance R1234 is found by finding
R23 = R2 + R3
Then
R234 = R4 || R23
Then
R1234 = R1 + R234

Then I = E/R1234
 

1. What is a circuit?

A circuit is a closed loop through which electric current can flow. It typically consists of a power source, conductors, and loads such as resistors, capacitors, and inductors. The flow of electric current can be controlled and manipulated within a circuit to power various devices.

2. What is a resistor?

A resistor is an electrical component that resists the flow of electric current. It is typically made of a material that has high resistance, such as carbon or ceramic. Resistors are used in circuits to control the amount of current that flows through a circuit and to regulate voltage levels.

3. How does a resistor affect a circuit?

A resistor affects a circuit by reducing the amount of current that flows through it. This is known as resistance, and it is measured in ohms. The higher the resistance, the lower the current that can flow through the circuit. This can be useful for controlling the power and voltage levels in a circuit.

4. What is the difference between a series and parallel circuit?

In a series circuit, the components are connected in a single loop, with the current flowing through each component in succession. In a parallel circuit, the components are connected in separate branches, with the current dividing and flowing through each branch simultaneously. This results in different current and voltage levels in each type of circuit.

5. How do you calculate the total resistance in a series or parallel circuit?

In a series circuit, the total resistance is equal to the sum of the individual resistances. For example, if there are three resistors in series, the total resistance would be the sum of those three values. In a parallel circuit, the total resistance is calculated differently depending on whether the resistors are in parallel or a combination of series and parallel. It is important to use the correct formula for the type of circuit being analyzed.

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