Make a rule: how would you find the resistance of a parallel circuit with

Make a rule: how would you find the resistance of a parallel circuit with n identical resistors?

2 months ago

Solution 1

Guest Guest #4093
2 months ago
When n resistors are connected in parallel, it means they are connected to the same potential difference V:
V=V_1 =V_2 =...=V_n (2)
It also means that the total current in the circuit is given by the sum of the currents flowing through each branch (each resistor) of the circuit:
I=I_1+I_2 +...+I_n (1)

By using Ohm's law:
I= \frac{V}{R}
we can rewrite (1) as
 \frac{V}{R_{eq}} =  \frac{V_1}{R_1}+ \frac{V_2}{R_2}+...+ \frac{V_n}{R_n}
However, we said that the potential difference across each resistor is equal (eq.(2)), so we can rewrite the last formula as
 \frac{V}{R_{eq}} = \frac{V}{R_1}+ \frac{V}{R_2}+...+ \frac{V}{R_n}
From which we find an expression for the equivalent resistance of n resistors in parallel:
 \frac{1}{R_{eq}}= \frac{1}{R_1}+ \frac{1}{R_2}+....+ \frac{1}{R_n}

📚 Related Questions

A cello string 0.75 m long has a 220 hz fundamental frequency. find the wave speed along the vibrating string. answer in units of m/s.
Solution 1
For fundamental frequency of a string to occur, the length of the string has to be half the wavelength. That is,

1/2y = L, where L = length of the string, y = wavelength.

y = 2L = 2*0.75 =1.5 m

y = v/f Where v = wave speed, and f = ferquncy

v = y*f = 1.5*220 = 330 m/s
A car has two horns, one emitting a frequency of 199 hz and the other emitting a frequency of 203 hz. what beat frequency do they produce?
Solution 1
Beat frequency, fb = |f2-f1|

That is, beat frequency is the absolute difference between two frequencies. Is is as a results of destructive and constructive inferences.

Therefore, in this case:

fb = 203 - 199 = 4 Hz
Extend your thinking: household appliances are usually connected in a parallel circuit. why do you think it might be a problem if too many appliances are turned on at once? (hint: current in a wire also produces heat.)
Solution 1

There might be a problem of a lot of power being dissipated if too many

appliances are turned on at once.

We can infer from Ohm's law that as resistance decreases, the total current increases.

I= V/R

The power dissipated through the circuit is directly proportional to the square

of the current.

P= I²R

We can therefore state that the power dissipated via heat will be much when

too many appliances are turned on at once.

Read more about Electricity here

Solution 2
The equivalent resistance of several devices connected in parallel is given by
 \frac{1}{R_{eq}} =  \frac{1}{R_1}+ \frac{1}{R_2}+...+ \frac{1}{R_n}
where R_i are the resistances of the various devices. We can see that every time we add a new device in parallel, the term  \frac{1}{R_{eq}} increases, therefore the equivalent resistance of the circuit R_{eq} decreases.

But Ohm's law:
I= \frac{V}{R_{eq}}
tells us that if the equivalent resistance decreases, the total current in the circuit increases. The power dissipated through the circuit (and so, the heat produced) depends on the square of the current:
P=I^2 R
therefore if there are too many devices connected in parallel, this can be a problem because there could be too much power dissipated (and too much heat) through the circuit.
Apply: what will be the total resistance and current in a parallel circuit with a 15-volt battery and three 10-ohm resistors? test your answers with the gizmo.
Solution 1
1) Total resistance

the total resistance of a circuit with n resistors in parallel is given by
 \frac{1}{R_{eq}} =  \frac{1}{R_1}+ \frac{1}{R_2}+...+ \frac{1}{R_n}
where R_i are the single resistances.

In our circuit, we have 3 resistors of 10.0 \Omega each, so the total resistance of the circuit is given by
 \frac{1}{R_{eq}}= \frac{1}{10 \Omega}+ \frac{1}{10 \Omega}+ \frac{1}{10 \Omega}= \frac{3}{10 \Omega}
which means a total resistance of
R_{Eq} =  \frac{10 \Omega}{3}=3.33 \Omega

2) Current in the circuit

The current in the circuit can be found by using Ohm's law:
I= \frac{V}{R_{Eq}}
where V is the voltage of the battery and Req is the total resistance we found before. By using V=15 V, we find
I= \frac{15 V}{3.33 \Omega}=4.5 A
Lion and leopard are two of Africa's large cat ____.
Solution 1
The fill in blank would be breeds.
Lions and leopards are both cats, but they are different kinds.

I hope this helps! Let me know if you need further explanation.
What is an advantage of using coal power over solar power to generate electricity
Solution 1

An advantage of using coal power over solar power to generate electricity is Reliable Fuel.

Compared to solar power or wind energy, coal is a reliable, predictable, and dependable fuel. While it may not be at the forefront of national energy production, it can provide invaluable backup service and highly reliable fuel.

What is coal power ?

"Coal-fired power plants burn coal to make steam and the steam turns turbines (machines for generating rotary mechanical power) to generate electricity." Many industries and businesses have their own power plants, and some use coal to generate electricity for their own use and mostly in combined heat and power plants.

What is solar power ?

"Solar power works by converting energy from the sun into power." There are two forms of energy generated from the sun for our use – electricity and heat. Both are generated through the use of solar panels, which range in size from residential rooftops to 'solar farms' stretching over acres of rural land.

Know more about coal power here


Solution 2


Coal power can be generated at night


Which of the following statements about nuclear power is true? A. Nuclear power plants are cheap to build, but expensive to operate. B. Nuclear power plants are more expensive to operate than fossil fuel power plants. C. Nuclear power plants can cause thermal pollution in nearby lakes. D. Nuclear power plants emit carbon dioxide, sulfur dioxide, and nitrogen oxides which pollute the air.
Solution 1
I think the answer may be d I'm not completely sure 
Solution 2

the answer is A. for me

if Brian has 50 apples how many apples does he have now , sorry just needed to change my question
Solution 1
50 bc he HAS 50 so he STILL HAS IT
How does natural selection result in adaptations in a species
Solution 1
An organism's "fitness" is measured by its ability to live long enough to reproduce and pass down traits to their offspring. In sexually reproducing organisms, those who are most fit are most likely to survive often have a specialized trait that gave them the advantage in doing so. The organism with the traits that allowed them to survive and reproduce passes the trait to it's offspring. Assuming that the environment doesn't overly change, those offspring have a greater chance to survive and reproduce themselves. Thus, this trait becomes a specialized adaption for the environment and allows the species as a whole to survive longer.
I need help finding the answer: When a guitar string plays the note "A", the string vibrates at 440 Hz. What is the period of the vibration?
Solution 1
The formula applicable:

Period, T = 1/f --- Where T = period (s), and f = frequency (Hz).

Substituting by use of the values of frequency given in the current scenario,

T = 1/440 = 2.27*10^-3 seconds