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Theory & Procedure, Equivalent Resistance of Resistors (Parallel) Notes | Study Science Class 10 - Class 10

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Our Objective

To determine the equivalent resistance of two resistors when connected in parallel.

The Theory

Before we start learning about parallel circuits, we need to know what electrical circuits are and about  the types of circuits!

Electrical Circuit

An electric circuit is simply a closed loop through which charges can continuously move. An electric circuit basically contains a source of electricity, a load resistance, a switch or a key for turning the circuit on or off at one's convenience.

The diagrammatic representation of an electric circuit is called the circuit diagram.  

Theory & Procedure, Equivalent Resistance of Resistors (Parallel) Notes | Study Science Class 10 - Class 10

 

Types of circuits

When two or more resistors are connected in such a way that one end of one resistance is connected to the starting end of the other, then the circuit is called Series Circuit.

Similarly, if the starting ends of two resistors are joined to a point, and the terminal ends of the two are combined and given connection to a source of electricity, those circuits are called Parallel Circuit.

Unlike in the series circuit, the current in each branch of a parallel circuit will be different. If one branch is broken, current will

Theory & Procedure, Equivalent Resistance of Resistors (Parallel) Notes | Study Science Class 10 - Class 10

continue flowing to the other branches.

At our homes all the electronic appliances are connected in parallel with each other.  This means they all get the full mains voltage, so that we can turn on the TV without having to turn on the microwave as well.

Before calculating the equivalent resistance, we need to know what resistance is?

Electrical resistance shows how much energy you need when you move the charges/current through your devices. If you need lots of energy, then the resistance required is also high.

Ie., the property of a conductor to oppose the flow of charges through it is called its resistance.
It is measured as resistanceTheory & Procedure, Equivalent Resistance of Resistors (Parallel) Notes | Study Science Class 10 - Class 10

ie., Theory & Procedure, Equivalent Resistance of Resistors (Parallel) Notes | Study Science Class 10 - Class 10

All metals are good conductors so all metal wires have a relatively low resistance.

The longer a piece of wire the higher is its resistance.  Double the length means double the resistance.

ie.,  Theory & Procedure, Equivalent Resistance of Resistors (Parallel) Notes | Study Science Class 10 - Class 10

The resistance of a piece of wire also depends on its thickness / cross-sectional area A of the conductor.  Double the area means half the resistance.  A thin wire has a higher resistance than the same thick piece.
ie., Theory & Procedure, Equivalent Resistance of Resistors (Parallel) Notes | Study Science Class 10 - Class 10

Finally, resistance of a piece of wire depends on its temperature also.  The higher the temperature the higher is the resistance. 

Calculating the effective resistance/total resistance of parallel circuits:

Calculating the equivalent resistance of two or more resistors in parallel is a little more complicated than calculating the total resistance of two or more resistors in series.
Given two resistors, Rand R2, in parallel, the equivalent resistance, Rt, is:

Theory & Procedure, Equivalent Resistance of Resistors (Parallel) Notes | Study Science Class 10 - Class 10

Theory & Procedure, Equivalent Resistance of Resistors (Parallel) Notes | Study Science Class 10 - Class 10

That is, for a set of parallel resistors, the reciprocal of their equivalent

resistance equals the sum of the reciprocals of their individual resistances.
Thus, resistance decreases in parallel combination.  
Using the formula is not too difficult.  Simply substitute  your values for the resistances and then add up the fractions. To find the equivalent resistance (Rt), you need to upside down your result.
Here, we used Meter Bridge to calculate the effective resistance accurately.
The Meter Bridge is a device for measurement of resistance using the principle of Wheatstone Network.

So, go ahead and try out the experiment as per the procedures and find the equivalent resistance!!


Materials Required: 

Theory & Procedure, Equivalent Resistance of Resistors (Parallel) Notes | Study Science Class 10 - Class 10

Procedure: 

As performed in the real lab: 

  1. Make a circuit as shown in the figure.
  2. Ensure that all the connections should be tight.
  3. Check whether the connections are correct by taking out some resistance from the resistance box and close the plug key ‘K’.
  4. Press the jockey at the left extreme of the metre bridge. Mark the direction of the deflection on the galvanometer. Again press the jockey at right extreme of the metre bridge and mark the direction of the deflection again. If the directions of the deflections are in opposite direction, then the connections are correct, otherwise check the connections.
  5. The balancing point is obtained by sliding the jockey along the wire and when there is no deflection in the galvanometer.
  6. Take at least three sets of observations by moving the jockey from both the end of the bridge for each wire and also when it is connected parallel.
  7. To make the parallel connection, just join one end of each resistor to a common point and connect in the right gap of the metre bridge.
  8. Record your observations.
  9. Find its resistance of this combination as mentioned in the below observation table. 

As performed in the simulator:

Theory & Procedure, Equivalent Resistance of Resistors (Parallel) Notes | Study Science Class 10 - Class 10

  1. Your simulator will consist of a metre bridge kept on a table, battery, resistance box and wires on the side bar menu.
  2. You can calculate the resistance of a single wire or serially connected wire by selecting from the drop down menu, “Arrangement of Resistors”.
  3. If you selected, “Single”, then drag the battery and the resistance box shown on the side bar menu near to the metre bridge using your mouse.
  4. Drag one of the wires to the right gap of the metre bridge.
  5. Now the button, “Start experiment” will be enabled.
  6. Now you can select your desired resistance from the resistance box just by clicking on the box and then choosing the resistance from the pop-window, “Select Resistance”. Now close the pop-window.
  7. Click on the enabled button and "Insert Key”.
  8. Now you can move the jockey from one left end to right either by moving the jockey with your mouse or by moving the slider, “Jockey Position”.
  9. Simultaneously check the readings of the galvanometer, once the needle reaches the zero reading, stop moving the jockey and note down the length of the wire from the balanced position on the left side, let say “AB” which is l cm.
  10. Repeat the same by moving the jockey from the right end to the left and note down the length of the wire from the balanced position on the right side, let take it as “BC” which is (100-l) cm.
  11. Repeat the same procedure with second wire and note down the lengths.
  12. For each wire take three readings and calculate its mean readings/resistance.
  13. Repeat the same procedures for the parallel connection. (Here, you need to drag the wire twice to make a parallel connection).

Observation: 

Table for Length (l) and Unknown Resistance (X) 


Resistance coil
Serial No. of Obs.
Resistance from the resistance box R (ohm) 
Length

Theory & Procedure, Equivalent Resistance of Resistors (Parallel) Notes | Study Science Class 10 - Class 10

(cm)
 
Length

Theory & Procedure, Equivalent Resistance of Resistors (Parallel) Notes | Study Science Class 10 - Class 10

(cm)
 
Resistance
Theory & Procedure, Equivalent Resistance of Resistors (Parallel) Notes | Study Science Class 10 - Class 10
(ohm)
Mean resistance (ohm)
 r1 only
1.
2.
3.
 
 
 
 
  r1 =...........
 r2 only
1.
2.
3.
 
 
 
 
  r2 =...........
r1 and r2 in parallel 
1.
2.
3.
 
 
 
 
  Rp =...........


Calculations:

  1. Calculation for r1 only, ronly, rand rin parallel
     
  2. Calculation for verification of laws in parallel:

    Experimental value of R= ........... ohm

    Theoretical value of   

    Theory & Procedure, Equivalent Resistance of Resistors (Parallel) Notes | Study Science Class 10 - Class 10          = ........... ohm

                                                      Difference (if any) = .......... ohm 

Result: 

Within the limits of experimental error, experimental and theoretical values of Rp are same. Hence, law of resistances in parallel is verified.

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