How Do You Calculate Total Resistance in Mixed Resistor Circuits?

In summary, the conversation discusses a circuit problem involving resistors in parallel and series. The correct formula for finding the total resistance of resistors in parallel is mentioned and it is clarified that the given formula is incorrect. The conversation also delves into the use of voltmeters in the circuit and how they will read the same potential difference over each resistor in series.
  • #1
shihab-kol
119
8

Homework Statement


upload_2017-8-21_16-41-58.png


2. Homework Equations [/B]
## V = IR ##

The Attempt at a Solution


My solution:
R1,R2,R3 are in parallel and so we can find their total R

## \frac {R1×R2×R3}{R1+R2+R3} = R'##

##R' = \frac {10}{3}##
R' is in series with R4

## ∴ R= R' + R4 = \frac{10}{3} +10 = \frac{40}{3}\Omega ##

We find current to be ,
$$I=\frac{3}{4} A ------(From ~Ohm's~ Law)$$
## V ~across~ R1,R2,R3 ~is~ same ~and ~I~ across ~R'~ and ~R ~is ~same##

$$∴ V'=I×R'=\frac{3}{4}×\frac{10}{3}=\frac {5}{2}$$

Similarly, we find for the other.

Is my process alright ?
 
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  • #2
shihab-kol said:
R1,R2,R3 are in parallel...

Are they? Review the definition of circuit elements in parallel.
 
  • #3
lewando said:
Are they? Review the definition of circuit elements in parallel.
Is it that R2,R3 Are in parallel and R1 is not?
 
  • #4
shihab-kol said:
R1,R2,R3 are in parallel and so we can find their total R
Remove the voltmeters and trace the path of current from A to B. What can you say about the current through the resistors?

shihab-kol said:
R1×R2×R3R1+R2+R3=R′R1×R2×R3R1+R2+R3=R′ \frac {R1×R2×R3}{R1+R2+R3} = R'
Even if the resistors were in parallel, this formula is incorrect. It has the dimensions of R2 and not R.
 
  • #5
cnh1995 said:
Remove the voltmeters and trace the path of current from A to B. What can you say about the current through the resistors?Even if the resistors were in parallel, this formula is incorrect. It has the dimensions of R2 and not R.
Removing voltmeters and included wires it is a series combo.
I couldn't understand the second part .
 
  • #6
shihab-kol said:
Removing voltmeters and included wires it is a series combo.
Yes.
(But just remove the voltmeters. Don't replace them with wires. This is because ideal voltmeters don't draw any current i.e. they act as open circuits. )

shihab-kol said:
I couldn't understand the second part .
The formula you used is incorrect. Look up the correct formula. (Not for this problem of course).

So if the resistors are in series, what will each voltmeter read?
 
  • #7
maybe it will be clearer if you draw the series connection of the four resistors in one straight line and then connect the voltmeters over the various parts of the circuits?
 
  • #8
What would the potential difference be over each of the resistors since they are in series with each other?
a voltmeter has a very high resistance so you could ignore them, they do not alter or influence the resistor circuit in any way.
 
  • #9
I have not thought about it but on its face since resistance is same as well as current each well have the same reading.
 
  • #10
shihab-kol said:
I have not thought about it but on its face since resistance is same as well as current each well have the same reading.
Really? Does #4 read the same as the rest? What voltage does #2 read? I suggest you redraw the circuit and rethink your answer.
 
  • #11
yes, the potential difference over each resistor will be the same. what should it be?
 
  • #12
andrevdh said:
yes, the potential difference over each resistor will be the same. what should it be?
I said NOTHING about the potential resistance over each resistor. My comment was about what the voltmeters will read.
 
  • #13
sorry, yes, I was communicating with shihab-kol
 
  • #14
andrevdh said:
sorry, yes, I was communicating with shihab-kol
To avoid such confusion, use the quote button so everyone know what post you are responding to.
 
  • #15
will do
 

Related to How Do You Calculate Total Resistance in Mixed Resistor Circuits?

1. What is the purpose of a resistor?

A resistor is an electronic component that is used to restrict the flow of electric current in a circuit. It is used to control the amount of current that passes through a circuit and can also be used to reduce the voltage in a circuit.

2. How do you calculate the resistance of a resistor?

The resistance of a resistor can be calculated using Ohm's Law, which states that the resistance (R) is equal to the voltage (V) divided by the current (I). This can be represented by the equation R = V/I. The unit of resistance is measured in ohms (Ω).

3. What is the difference between series and parallel circuits?

In a series circuit, the components are connected in a single loop, so the current has only one path to flow through. In a parallel circuit, the components are connected in multiple branches, so the current has multiple paths to flow through. This results in different voltage and current values in each type of circuit.

4. How do voltmeters work?

A voltmeter is an instrument used to measure the voltage in a circuit. It works by connecting the two leads of the voltmeter in parallel with the component or portion of the circuit that you want to measure. The voltmeter then measures the potential difference between the two points and displays the voltage on a scale.

5. Can voltmeters be used to measure current?

No, voltmeters cannot be used to measure current directly. They are designed to measure voltage, not current. To measure current, a separate instrument called an ammeter is used. However, voltmeters can indirectly measure current by using Ohm's Law and measuring the voltage drop across a known resistor in the circuit.

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