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The flow of charged particles, known as electric current, contains stable and constant flow from higher to lower potential in a circuit. A regular circuit consists of conductors, resistors, power source, switch to turn on and switch to turn off.
A resistor is a fundamental electronic component to be used to convert a voltage to a current and vice-versa. It mainly provides resistance or limits the flow of current in a circuit. A different weighting can be placed on to the converted current/voltage by adjusting the resistors’ value properly which allows it to be useful in voltage reference circuits and applications.
Individual resistors can be used in different ways to create a more complex resistor network whose equivalent resistance will be the mathematical combination of the used individual resistors. Resistors can be connected in three ways - Series connection, Parallel connection, Combination of series and parallel connection. Regardless of any complexity, all resistors follow the basic rules as prescribed by Ohm’s Law and Kirchhoff’s Circuit Laws. Resistors in series or complex resistor networks can be replaced with a single equivalent resistor.
Read more : Important Formula in electricity
Key Terms: Resisters, Resisters in Series, Resisters in Parallel, Series and parallel Combinations of Resistors
Resistors in Series
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Single resistors connected in a daisy chain pattern together in a single line are known as connected in ‘Series’. The current flows in resistors in series have a common flow as it doesn’t have any other way except flowing through the first resistor, then passing through the second, third and so on. This means the current flowing in resistors in series has only one path to take. Thus, all the resistors connected in a daisy-chained series have a common current flow.
A voltage drop will always be there across a series of resistors. Ohm’s law is used to calculate the equivalent resistance of a series of resistors.
When 3 Resistors are connected in a series:
- Across the circuit, the same current flows which can be denoted as ‘I’.
- The potential difference of each resistor of a series of resistors is equal to the potential difference of the whole set of resistors connected in a series.
The potential differences of three different resistors are V1,V2 and V3.
Then total potential difference V = V1+V2+V3
Read more : Difference between resistance and resistivity
This means the total potential difference is equal to the voltage of the battery.
- Total resistance will be equal to the summation of the resistance of individual resistors of a series.
R=R1+R2+R3
Resistance Formula for Series Circuit
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Suppose 3 resistors - R1, R2, R3 are connected in a series circuit.
The current of the circuit = I
The voltage of the circuit = Voltage of R1+ Voltage of R2+Voltage of R3
Voltage of R1 = V1 = IR1
Voltage of R2 = V2 = IR2
Voltage of R3 = V3 = IR3
We know, Total Voltage= Total Current x Total Resistance
Total Current = I (mentioned before)
Total Voltage= I x Total Resistance
Now,
V1+V2+V3 =Total voltage
IR1+IR2+IR3 = I x Total Resistance
I x (R1+R2+R3) = I x Total Resistance
Thus, Total Resistance = R1+R2+R3
That is why it is said that the sum of individual resistors of a series circuit is equal to the resistance of the whole circuit.
Usability of Resistors
- Use of more than one resistor in a circuit increases the total resistance of the circuit.
- More resistors limit the flow of current in a circuit.
Read more : Insulators
Important Points about Series of Resistors
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- The total resistance of a circuit is always greater than the resistance of an individual resistor of the same circuit.
- Produced resistance is highest in a series circuit of resistors.
- The Ammeter, connected to the series circuit, detects the amount of the net current flow in the circuit.
Read more : Resistors in parallel
Parallel Combination of Resistors
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- In the parallel combination of resistors, the flow of current gets divided to flow through different branches of the circuit.
- The voltage drop in each resistor is equal.
- The total resistance of the parallel circuit can be derived through Ohm’s Law and Kirchhoff’s Law.
According to Kirchhoff’s Law:
Iin = Iout
I = I1+I2
I = V1/R1 + V2/R2 = V/R1 + V/R2
I = V (1/R1 + 1/R2)
Rp = (1/R1 + 1/R2)-1
Thus, the resistors of parallel circuit formula is -
Rp = (1/R1 + 1/R2 + 1/R3 + .... + 1/RN-1+1/RN)-1
Read more : Conductors
Combination Resistors in Series and Parallel
- In reality, it’s hard to find an electric circuit having resistors placed in only parallel or series patterns. All electric circuits are a complex combination of resistors linked in parallel and series patterns.
- To calculate the resistance of such circuits we need to break the complex structure into small simple circuits.
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Sample Question
Ques. A circuit consists of 5 resistors having a voltage of 9V. Calculate the current ‘I’ through the resistors and the equivalent resistance.(3 marks)
Ans. Seeing the given figures, it can be understood that the resistors are in series. So, the series resistance formula will be used to figure out the equivalent resistance.
Given: V = 9V
R1 = R2 = R3 = R4 = 20 Ω
R5 = 10 Ω
The equivalent resistance = Rs
Rs = R1 + R2 + R3 + R4 + R5 = 20Ω + 20Ω + 20Ω + 20Ω+ 10Ω = 90Ω
Total resistance of significant digits is Req = 90Ω
Current of the circuit will be calculated by Ohm’s Law -
I = V/Rs = 9V/90Ω = 0.1A
Ques. Three resistors joined in series in a circuit having resistance 20Ω, 30Ω and 40Ω respectively. The potential difference of the circuit is 360V. What is the total resistance and current through the circuit? (2 marks)
Ans. Given, R1 = 20Ω, R2 = 30Ω, R3 = 40Ω and V = 360V
According to Ohm’s Law,
Total resistance R = R1 + R2 + R3 = 20Ω + 30Ω + 40Ω = 90Ω
We know,
I = V/R
I = 360V/90Ω = 4A
Thus, total resistance = 90Ω and Current through circuit = 4A
Ques. (i) Draw a closed circuit diagram consisting of a 0.5 m long nichrome wire XY, an ammeter, a voltmeter, four cells of 1.5 V each and a plug key.
(ii)Following graph was plotted between V and I values.What would be the values of V /I ratios when the potential difference is 0.8 V, 1.2 V and 1.6 V respectively?
(iii) What conclusion do you draw from these values? (3 marks)
Ans.(i)
(ii)
(iii) Conclusion: If I be the current through XY resistor and V be the potential difference across
Ques. What is meant by electric current? Name and define its SI unit. In a conductor electrons are flowing from B to A. What is the direction of conventional current? Give justification for your answer. A steady current of 1 ampere flows through a conductor. Calculate the number of electrons that flow through any section of the conductor in 1 second. (Charge on electron 1.6 X 10-19 coulomb). (3 marks)
Ans.
- Electric Current: The amount of charge ‘Q’ flowing through a particular area of cross section in unit time ‘t’ is called electric current, i.e.
- Electric current, I = Q/t
- The SI unit of electric current is ampere.
- One ampere of current is that current which flows when one coulomb of electric charge flows through a particular area of cross-section of the conductor in one second, i.e. 1A = 1 Cs-1.
- The direction of conventional current is A to B, i.e. opposite to the direction of flow of electrons. In a metal, flow of electrons carrying negative charge constitutes the current. Direction of flow of electrons gives the direction of electric current by convention, the direction of flow of positive charge is taken as the direction of conventional current. Charge = q = ne
Ques. Name a device that helps to maintain a potential difference across a conductor. (1 mark)
Ans. Cell or battery
Ques. Write S.I. unit of resistivity. (1 mark)
Ans. Ohm-metre (Ωm)
Ques. Write relation between heat energy produced in a conductor when a potential difference V is applied across its terminals and a current I flows through for ‘t’. (1 mark)
Ans. Heat produced, H = VIt
Ques. State difference between the wire used in the element of an electric heater and in a fuse wire. (1 mark)
Ans. The wire used in the element of electric heater has a high resistivity and has a high melting point, i.e. even at a high temperature element does not burn while fuse wire has a low melting point and high resistivity.
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