Basic Concepts
Electrical circuit
connect power supplies to loads such as resistors, capacitors, motors,
heaters, or lamps.
is a conducting path, external to the battery, which allows charge to flow from one terminal to the other. A simple circuit might consist of a single strand of metal wire linking the positive and negative terminals. A more realistic circuit possesses multiple branch points, so that charge can take many different paths between the two terminals.
The Circuit Elements
A
node is a point in a circuit where three or more elements are soldered together
A
branch is a current path between two nodes. Each branch in a circuit can have only one
current in it although a branch may have no current.
A
loop is a closed path that may consist of different branches with different currents in each branch.
A
Direct current (DC) circuit is a circuit is which the current through each branch in the
circuit is always in the same direction. When the power supply is steady in time, and then
the circuit is a purely resistive network then the current in each branch will be steady, that
is the currents will not vary in time. See the Example below.
Current
- Current (I) is the rate of flow of Charge Carriers, such as electrons. Current is usually thought of as moving in the direction of positive charge, so from the positive power supply to the negative. However, since in metals it is electrons that carry electric charge, the actually flow is opposite to the way in which we think of it.
- Current it the the amount of Charge, Q that passes a point in a set time, t. It is measured in Amps (A), and charge is measured in Coulombs (C). Since Amps are SI base units, Coulombs are defined as A×s, As.
Voltage
- Voltage (V) or Potential Difference (p.d.) is a measure of the Energytransferred per Charge Carrier between two points.
- Voltage is the Energy, E per Charge, Q. Voltage is measured in Volts (V), which is defined as one Joule per Coulomb. Voltage can be defined in base units as Kgm2s-3A-1.
Power
- Power (P) is the rate of Energy transfer. It is measured in watts (W), where one watt is defined as one Joule per Second. Hence watts can be expressed in base units as Kgm2s-3
- From this definition of Power, we can substitute the algebraic definitions above to produce a variety of other formulae, including 'Power = Current × Voltage'
- Ohm's Law states that 'Voltage = Current × Resistance'. We can use this to produce two more definitions of Power.
SERIES
Resistors in Series.
Resistors are said to be connected in “Series“, when they are daisy chained together in a single line.
Equation: Rtotal = R1 + R2 + R3 + ….. Rn etc.
Example:
Solution:
As the resistors are connected together in series the same current passes through each resistor in the chain and the total resistance, RT of the circuit must be equal to the sum of all the individual resistors added together. That is
RT=R1 + R2 + R3
and by taking the individual values of the resistors in our simple example above, the total equivalent resistance, REQ is therefore given as:
REQ = R1 + R2 + R3 = 1kΩ + 2kΩ + 6kΩ = 9kΩ
PARALLEL
Resistors in Parallel
Resistors are said to be connected together in “Parallel” when both of their terminals are respectively connected to each terminal of the other resistor or resistors. Unlike the previous series resistor circuit, in a parallel resistor network the circuit current can take more than one path as their are multiple nodes. Then parallel circuits are current dividers.
So we can define a parallel resistive circuit as one where the Resistors are connected to the same two points (or nodes) and is identified by the fact that it has more than one current path connected to a common voltage source. Then in our parallel resistor example below the voltage across resistor R1 equals the voltage across resistor R2 which equals the voltage across R3 and which equals the supply voltage. Therefore, for a parallel resistor network this is given as:
In the following resistors in parallel circuit the resistors R1, R2 and R3 are all connected together in parallel between the two points A and B as shown.
Parallel Resistor Circuit
In the previous series resistor network we saw that the total resistance, RT of the circuit was equal to the sum of all the individual resistors added together. For resistors in parallel the equivalent circuit resistance RT is calculated differently.
Here, the reciprocal ( 1/R ) value of the individual resistances are all added together instead of the resistances themselves with the inverse of the algebraic sum giving the equivalent resistance as shown.
Parallel Resistor Equation
Then the inverse of the equivalent resistance of two or more resistors connected in parallel is the algebraic sum of the inverses of the individual resistances.
We now know that resistors that are connected between the same two points are said to be in parallel. But a parallel resistive circuit can take many forms other than the obvious one given above and here are a few examples of how resistors can be connected together in parallel.
Find the total resistance, RT of the following resistors connected in a parallel network.
The total resistance RT across the two terminals A and B is calculated as:
Learnings:
I Learn how Solve Current and Resistors when theres a voltage in a series and a parallel using V=IR. Also to get the Power.
