Solve Current Divider Rule for Resistor Currents w/ R & i

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In summary, the conversation is about calculating the current through each resistor in a parallel network with three resistors of varying resistance (4 ohms, 2 ohms, and R). The current divider rule is used to find the current through each resistor, and the effective resistance of the parallel combination is needed to calculate the total current and voltage. The final answer is i_1 = i_0(R_2 + R_3/R_total), i_2 = i_0(R_3/R_total), and i_3 = i_0(0/R_total) = 0.
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jti3066
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Homework Statement



Three resistors with resistance 4 ohms, 2 ohms, and R are connected in parallel. There is a total current i through the network. Find the current through each resistor in terms of R and i.

Ignore the 4 ohms and 2 ohms for now I just need help with the CDR formula...Thanks

Homework Equations



i_0 = i_1 + i_2 + i_3

V = V_1 + V_2 + V_3

V_n = i_n * R_n


The Attempt at a Solution



Following the current divider rule I came to the "answer":

i_n = i_0(R_total/R_n)

so for example

i_1 = i_0((R_1 + R_2 + R_3)/R_1)

However my example problem states that the answer should be:

i_1 = i_0(R_2/(R_1 + R_2 + R_3))...?
 
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  • #2
Wait...is this correct?

i_1 = i_0(R_2 + R_3/R_total)

i_2 = i_0(R_3/R_total)

i_3 = i_0(0/R_total) = 0 because there are no resistor to the right of R_3
 
  • #3
What's the effective resistance of the parallel combination of three resistors? Call them R1, R2, R3.

Since the total current through the parallel group given as i, what's the voltage across all three? And, given the voltage across all three, you are now in a position to calculate the current though each, right?
 

What is the Current Divider Rule?

The Current Divider Rule is a formula used to calculate the current flowing through individual resistors in a parallel circuit. It states that the current through a specific resistor is equal to the total circuit current multiplied by the ratio of the resistor's resistance to the total resistance of the circuit.

How do you apply the Current Divider Rule?

To apply the Current Divider Rule, you must first identify the resistors in parallel in the circuit. Then, use the formula IR = (IT * RT) / R, where IR is the current through the specific resistor, IT is the total circuit current, RT is the sum of all the resistances in parallel, and R is the resistance of the specific resistor.

What are the limitations of the Current Divider Rule?

The Current Divider Rule only applies to parallel circuits with resistors. It does not work for series circuits or circuits with other types of components. Additionally, it assumes that the resistors are identical and have a constant resistance. In real-world circuits, this may not always be the case.

Can the Current Divider Rule be used for any number of resistors in parallel?

Yes, the Current Divider Rule is applicable for any number of resistors in parallel. It is a general formula that can be used for two or more resistors in parallel.

How does the Current Divider Rule help in practical applications?

The Current Divider Rule is useful in designing and analyzing parallel circuits, as it allows for the calculation of individual resistor currents. This information can be used to determine the power dissipation and voltage drops across each resistor, which is important for circuit design and troubleshooting. It is also used in electronic devices to control the flow of current and prevent damage to components.

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