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 = R1 + R2 + R3 + R4 + …………….. Rn
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 R1, R2, & R3 connected in series combination with a power supply of voltage.
    Potential difference of each resistor is V1, V2, & V3 respectively. Let electric current I is passing through     the circuit.
    Now
V = V1 + V2 + V3
According to Ohm’s law V = IR
thus
IRe = IR1 + IR2 + IR3
IRe = I(R1 + R2 + R3)
IRe/I = R1 + R2 + R3
Re = R1 + R2 + R3
    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 R1 , R2 & R3 connected in parallel combination with a power supply of voltage     V.
    Now
I = I1 + I2 + I3
    according to Ohm’s law
V/R = I
Therefore,
V/Re = V/R1 + V/R2 + V/R3
V/Re = V(1/R1 + 1/R2 + 1/R3)
V/ReV = 1/R1 + 1/R2 + 1/R3
OR
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