Solve R1 in Rt = R3 + [ ( 1/R1 + 1/R2 ) ^-1 ] for Parallel Circuits

In summary, the equation Rt = R3 + [ ( 1/R1 + 1/R2 ) ^-1 ] represents the total resistance in a parallel circuit, which is the combined resistance of all components. The total resistance is less than the individual resistances due to multiple paths for current flow. The ^-1 exponent represents the inverse function, necessary for accurate calculation. To solve for R1, algebraic manipulation is used. This equation is widely used in the design and analysis of electrical circuits, essential in various fields of science such as engineering and physics.
  • #1
aks333
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Homework Statement



Rearrange formula for series and parallel circuit combination.
Make R1 the subject of the formula : Rt = R3 + [ ( 1/R1 + 1/R2 ) ^-1 ]

Homework Equations



Rt = R3 + [ ( 1/R1 + 1/R2 ) ^-1 ]

The Attempt at a Solution



I am unsure as to how to get rid of the inverse? please help.
 
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  • #2
Rt = R3 + ( 1/R1 + 1/R2 )-1

Rt - R3 = ( 1/R1 + 1/R2 )-1

1/(Rt - R3) = 1/R1 + 1/R2

Continue...
 

What does the equation Rt = R3 + [ ( 1/R1 + 1/R2 ) ^-1 ] represent?

The equation represents the total resistance (Rt) in a parallel circuit, which is the combined resistance of all the components in the circuit.

Why is the total resistance of a parallel circuit different from the individual resistances?

In a parallel circuit, the total resistance is less than the individual resistances because the current has multiple paths to flow through, reducing the overall resistance in the circuit.

What is the significance of the ^-1 exponent in the equation?

The ^-1 exponent represents the inverse function, which is necessary to calculate the total resistance in a parallel circuit. Without it, the equation would not accurately reflect the relationship between the individual resistances and the total resistance.

How do you solve for R1 in the equation for parallel circuits?

To solve for R1, you can use algebraic manipulation to isolate R1 on one side of the equation. This may involve distributing the inverse function, combining like terms, and using the inverse operation to isolate R1.

What is the practical application of this equation in the field of science?

This equation is commonly used in the design and analysis of electrical circuits, which is important in various fields of science such as engineering, physics, and electronics. It allows scientists to calculate the total resistance and analyze the behavior of parallel circuits, which is essential in understanding and predicting the performance of different electrical systems.

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