For
resistors in parallel with resistances
and
, the equivalent resistance is:
Equivalent parallel resistance
Consider a circuit consisting of a single cell and three resistors that are connected in parallel.
Using what we know about voltage and current in parallel circuits we can define the equivalent resistance of several resistors in parallel as:
Equivalent resistance in a parallel circuit,
For
resistors in parallel, the equivalent resistance is:
Let us apply this formula to the following circuit.
What is the total resistance in the circuit?
Experiment : current in parallel circuits
Aim:
To determine the effect of multiple resistors on current in a circuit
Apparatus:
Battery
Resistors
Light bulb
Wires
Method:
Construct the following circuits
Rank the three circuits in terms of the brightness of the bulb.
Conclusions:
The brightness of the bulb is an indicator of how much current is flowing. If the bulb gets brighter because of a change then more current is flowing. If the bulb gets dimmer less current is flowing.
You will find that the more resistors you have the brighter the bulb.
Why is this the case? Why do more resistors make it easier for charge to flow in the circuit? It is because they are in parallel so there are more paths for charge to take to move. You can think of it like a highway with more lanes, or the tube of marbles splitting into multiple parallel tubes. The more branches there are, the easier it is for charge to flow. You will learn more about the total resistance of parallel resistors later but always remember that more resistors in parallel mean more pathways. In series the pathways come one after the other so it does not make it easier for charge to flow.
Two
resistors are connected in parallel. Calculate the equivalent resistance.
Since the resistors are in parallel we can use:
The equivalent resistance of two
resistors connected in parallel is
.
Two resistors are connected in parallel. The equivalent resistance is
. If one resistor is
, calculate the value of the second resistor.
Since the resistors are in parallel we can use:
We are given the value of
and
.
The second resistor has a resistance of
.
Resistance
What is the unit of resistance called and what is its symbol?
Explain what happens to the total resistance of a circuit when resistors are added in series?
Explain what happens to the total resistance of a circuit when resistors are added in parallel?
Why do batteries go flat?
The following presentation summarizes the concepts covered in this chapter.
Exercises - electric circuits
Write definitions for each of the following:
resistor
coulomb
voltmeter
Draw a circuit diagram which consists of the following components:
2 batteries in parallel
an open switch
2 resistors in parallel
an ammeter measuring total current
a voltmeter measuring potential difference across one of the parallel resistors
Complete the table below:
Quantity
Symbol
Unit of meaurement
Symbol of unit
e.g. Distance
e.g. d
e.g. kilometer
e.g. km
Resistance
Current
Potential difference
Draw a diagram of a circuit which contains a battery connected to a lightbulb and a resistor all in series.
Also include in the diagram where you would place an ammeter if you wanted to measure the current through the lightbulb.
Draw where and how you would place a voltmeter in the circuit to measure the potential difference across the resistor.
Thandi wants to measure the current through the resistor in the circuit shown below and sets up the circuit as shown below. What is wrong with her circuit setup?
[SC 2003/11] The emf of a battery can best be explained as the
rate of energy delivered per unit current
rate at which charge is delivered
rate at which energy is delivered
charge per unit of energy delivered by the battery
[IEB 2002/11 HG1] Which of the following is the correct definition of the emf of a battery?
It is the product of current and the external resistance of the circuit.
It is a measure of the cell's ability to conduct an electric current.
It is equal to the “lost volts” in the internal resistance of the circuit.
It is the power supplied by the battery per unit current passing through the battery.
[IEB 2005/11 HG] Three identical light bulbs A, B and C are connected in an electric circuit as shown in the diagram below.
How bright is bulb A compared to B and C?
How bright are the bulbs after switch S has been opened?
How do the currents in bulbs A and B change when switch S is opened?
Current in A
Current in B
(a)
decreases
increases
(b)
decreases
decreases
(c)
increases
increases
(d)
increases
decreases
[IEB 2004/11 HG1] When a current
is maintained in a conductor for a time of
, how many electrons with charge e pass any cross-section of the conductor per second?
It
It/e
Ite
e/It
Questions & Answers
differentiate between demand and supply
giving examples
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product