COMBINATION
OF RESISTORS


.  
Resistance
can be joined to each other by two ways: 1. Series combination 2. Parallel combination 

SERIES
COMBINATION


Characteristics:  
1.
If different resistances are joined with each other such that there is only
one path for the flow of electric
current then the combination of such resistances is called Series Combination.
2. In series combination current through each resistor is constant. 3. In series combination Potential difference across each resistor is different depending upon the value of resistance. 4. Equivalent resistance of circuit is equal to the sum of individual resistances. 

Re
= R_{1} + R_{2} + R_{3} + R_{4} + ……………..
R_{n}


DISADVANTAGE


If one component is fused, then the other components of circuit will not function.  
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EQUIVALENT
RESISTANCE IN SERIES COMBINATION


Consider three resistances R_{1}, R_{2}, & R_{3} connected in series combination with a power supply of voltage.  
Potential difference of each resistor is V_{1}, V_{2}, & V_{3} respectively. Let electric current I is passing through the circuit.  
Now  
V = V_{1}
+ V_{2} + V_{3}


According to Ohm’s law V = IR
thus 

IRe
= IR_{1} + IR_{2} + IR_{3}
IRe = I(R_{1} + R_{2} + R_{3}) IRe/I = R_{1} + R_{2} + R_{3} Re = R_{1} + R_{2} + R_{3} 

This shows that in series combination equivalent resistance of circuit is always greater than individual resistances.  
PARALLEL
COMBINATION


Characteristics:
1. If there are more than one path for the flow of current in a circuit then the combination of resistances is called Parallel Combination. 2. In parallel combination current through each resistor is different. 3. Potential difference across each resistor is constant. 4. Equivalent resistance of circuit is always less than either of the resistances included in the circuit. 

ADVANTAGE


In parallel combination of resistors, if one component of circuit (resistor) is damaged then rest of the component of the circuit will perform their work without any disturbance. It is due to the presence of more than paths for the flow of electric current.  
EQUIVALENT
RESISTANCE IN PARALLEL COMBINATION


Consider three resistances R_{1} , R_{2} & R_{3} connected in parallel combination with a power supply of voltage V.  
Now  
I = I_{1}
+ I_{2} + I_{3}


according to Ohm’s law  
V/R
= I
Therefore, V/Re = V/R_{1} + V/R_{2} + V/R_{3} V/Re = V(1/R_{1} + 1/R_{2} + 1/R_{3}) V/ReV = 1/R_{1} + 1/R_{2} + 1/R_{3 OR } 

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