# Simple circuit - Finding Equivalent Resistance

• Engineering
• jmcmillian
In summary, the problem is asking to find the value of Vo in a circuit with a given current and resistors. The approach is to first find the equivalent resistance and then use it to calculate Io and finally Vo. The attempt to find the equivalent resistance involves adding resistors in series and simplifying the circuit. However, the 2k and 10k ohm resistors are not relevant since no current flows through them. The current divides itself proportionally through the two branches based on their conductances, and the potential drop across the branches is equal. The total resistance and potential can be calculated using standard formulae as a check.
jmcmillian

## Homework Statement

Find Vo in the circuit.
Image of Circuit Diagram Attached
Variables: Vo, Io
Given: Current (15 mA)
Resistors (300$$\Omega$$, 300$$\Omega$$, 2k$$\Omega$$, 10k$$\Omega$$, 200$$\Omega$$, 3k$$\Omega$$

## Homework Equations

Resistors in Series: Ra+Rb+Rc...+Rn
Resistors in Parallel: [(1/Ra)+(1/Rb)+(1/Rc)+...+(1/Rn)]^-1
V_j = I_j*R_j; I_j = R_eq*I

## The Attempt at a Solution

I've decided my approach in this problem should be:
(1) Find Equivalent Resistance (R_eq)
(2) Use the formula I_j=R_eq*I to determine I_o
(3) Use I_o to find V_o, as V_o= I_o*R_o

My problem is that I really am unsure how to find the equivalent resistance in this particular problem. What's messing me up is the 2k$$\Omega$$ and 10k$$\Omega$$ resistors...and the gap that is between them. I've just never done a circuit like this I guess.

My attempt to find the equivalent is below:
In Series, Left Side:300 and 300 ohm = 600 ohm
In Series, Right Side:200 and 1000 ohm = 1200 ohm
Simplified Resistor: 600 ohm on Left, 1200 ohm on right, 2k and 10k ohm on top.
The equivalent can be found by adding up in series: 600, 1200, 2000, and 10000 = 13,800ohms = 13.8kOhm. Is that correct? If not, how do I attack the equivalence problem?

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Hint :-

Suppress the current source and then analyze the circuit again.

Hope this is useful.

It may not correspond to systematic teachings, but the way automatic for me would be to say the 2k and 10k ohm resistors play no part in the problem since no current flows through them. The current merely divides itself flowing through the two branches proportionately to their conductances.

Work out how it divides itself.

There is the same potential drop for the two branches. The potential drop in two resistors in series (in either of the branches) is proportional to the resistance, e.g. it will be equal for the two resistors in the left-hand branch. Work out what it is in each case according to V = IR.

You can work out the total resistance of this circuit from standard formulae you should know and understand, and hence the total potential. Do this as a check, it should come out agreeing with (voltages added up in) previous results. I hope this is not telling you too much according to the rules.

Last edited:

## What is a simple circuit?

A simple circuit is a closed loop of conductive material that allows electricity to flow through it. It typically consists of a power source, such as a battery, wires to connect the components, and a load, such as a light bulb or resistor.

## What is equivalent resistance in a circuit?

Equivalent resistance is the combined resistance of multiple resistors in a circuit. It is the total resistance that the current must overcome to flow through the circuit. Equivalent resistance is calculated using Ohm's law, which states that resistance is equal to voltage divided by current.

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

In a series circuit, resistors are connected end-to-end, so the current must flow through each resistor in succession. To find the equivalent resistance, simply add up the individual resistances of each resistor in the circuit. This can be represented by the equation Req = R1 + R2 + R3 ...

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

In a parallel circuit, resistors are connected side by side, so the current can flow through each resistor simultaneously. To find the equivalent resistance, use the equation 1/Req = 1/R1 + 1/R2 + 1/R3 ... and then take the reciprocal of the result to find Req.

## Why is finding equivalent resistance important?

Finding equivalent resistance is important because it helps in understanding how a circuit behaves and how much current will flow through it. It can also be used to determine the power dissipated in a circuit, which is important for designing and troubleshooting electronic devices.

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