# Equivalent resistance of a circuit

• EchoTheCat
In summary, the conversation discusses the calculation of equivalent resistance in an electric circuit with various resistors. The total voltage, current, and resistance in both series and parallel circuits are explained. The solution involves combining resistors in a series and parallel arrangement to calculate the final equivalent resistance.
EchoTheCat

## Homework Statement

Consider the electric circuit shown in the figure. Assume that V = 13.7 V, R1 = R2 = R3 = R4 = R5 = 7.00 Ω. What is the equivalent resistance of the circuit?

## Homework Equations

total voltage of a series circuit is the sum of the voltage of all the resistors
total current of a series circuit is the same as the current through any individual resistor
total resistance of a series circuit is the sum of the resistance of all the resistors

total voltage of a parallel circuit is the same as the voltage through any individual resistor
total current of a parallel circuit is the sum of the current of all of the resistors
the inverse of the total resistance of a parallel circuit is the sum of the inverse of each resistance

## The Attempt at a Solution

I guess I'm confused as to how to 'combine' resistors to turn this into just a series circuit? I see both parallel elements and series elements.

Here's the picture.

I did try considering the circuit as a parallel circuit R1, R3, and R4 together with total resistance 21 and R2 and R5 together with total resistance 14 but that didn't work

#### Attachments

• circuit.PNG
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In this circuit, it is easiest to start at the tight and fold up the resistances right-to-left.

What 2 resistors are in series on the right side? What is their combined resistance? Then what other resistor is in parallel with that combined resistance? Combine those parallel resistances. Then finally, what 3 resistances are now in series? Combine them to get the answer.

Can you try that and show us your math for each step? Thanks.

Resistors 2 and 5 form a series circuit on the right side; their combined resistance is 14. This is parallel to Resistor 3; their combined resistance is 1/R = 1/7 + 1/14 --> R = 4.66667. The three resistors now in series are 1, 4, and combined resistors of 2, 3, and 5. The sum of the resistance is 4.66667 + 7 + 7 =18.66667 ohms.

And it works!
Thank you!

berkeman

## What is "Equivalent Resistance" in a circuit?

Equivalent resistance is the total resistance of a circuit as seen from a single point. It is the resistance that would produce the same amount of current flow in the circuit as the original combination of resistors.

## How do you calculate the equivalent resistance of a series circuit?

In a series circuit, the equivalent resistance is the sum of all the individual resistances. For example, if there are three resistors in a series, their equivalent resistance would be Req = R1 + R2 + R3.

## How do you calculate the equivalent resistance of a parallel circuit?

In a parallel circuit, the equivalent resistance is calculated using the formula 1/Req = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn, where Rn represents each individual resistance. The reciprocal of this value is the equivalent resistance of the parallel circuit.

## What is the difference between series and parallel circuits?

In a series circuit, the resistors are connected in a single path, while in a parallel circuit, the resistors are connected in multiple paths. In a series circuit, the current is the same at all points, while in a parallel circuit, the voltage is the same at all points.

## How do you calculate the equivalent resistance of a complex circuit?

In a complex circuit, where resistors are connected in both series and parallel, you can use a combination of the series and parallel resistance formulas to calculate the equivalent resistance. You can also use Kirchhoff's laws and Ohm's law to determine the equivalent resistance.

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