Blog

Combination of resistance – In different cases, a number of resistance are connected together in an electric circuit to perform different works. This is known as the combination of resistance.

Types of connection of resistance
(i) Series connection
(ii) Parallel Connection

(i) Series Connection –  In an electric circuit, a number of resistance are joined end to end consecutively so that same current flows through each, then the combination is called series connection.

In the series connection, the equivalent or total resistance (R) is given by

R = R₁ + R₂ + R₃

Derivation

According to ohm’s law

  V_AB = IR₁,        V_Bc = IR₂,        V_CD = IR₃

  Now the total potential of the circuit,

  (V) = V_AB + V_Bc + V_CD

  or,  IR =  IR₁ + IR₂ + IR₃

  or,  IR =  I(R₁ + R₂ + R₃)

  or, R = R₁ + R₂ + R₃

(ii) Parallel Connection – If in an electric circuit a number of resistors are joined by placing them side by side with corresponding ends joined together so that the main current is divided among them, then the connection is called parallel connection (or combination) of resistance.

In the parallel connection, the equivalent or total resistance (R) is given by

\frac { 1 }{ R } =\frac { 1 }{ { R }_{ 1 } } +\frac { 1 }{ { R }_{ 2 } } +\frac { 1 }{ { R }_{ 3 } }