Consider the following circuit: The equivalent resistance of the circuit will be
CONCEPT :
Resistance:
- The measurement of the opposition of flow of electric current through a conductor is called the resistance of that conductor.
- It is denoted by R.
- There are mainly two ways of the combination of resistances:
Series combination of the resistance:
- When two or more resistances are connected one after another such that the same current flows through them are called resistances in series .
- The net resistance/equivalent resistance (R) of resistances in series is given by:
⇒ R = R 1+ R 2 ...(1)
The parallel combination of the resistance:
- When the terminals of two or more resistances are connected at the same two points and the potential difference across them is equal is called resistances in parallel.
- The net resistance/equivalent resistance(R) of resistances in parallel is given by:
\(⇒ \frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}\;\;\;\;\; \ldots \left( 2 \right)\)
EXPLANATION :
Given: R 1 = 2 Ω, R 2 = 4 Ω, R 3 = 6 Ω
- The 2 Ω, 4 Ω, and 6 Ω are in parallel combination, the equivalent of these three will be;
- Using equation 2,
\(⇒ \frac{1}{R} = \frac{1}{2} + \frac{1}{4} + \frac{1}{6}\)
⇒ R = 12/11 Ω
- Now 12/11 Ω and 8 Ω are in series
- Using equation 1,
⇒ Rnet = 12/11 + 8
⇒ R net = 100/11 Ω = \(9\frac{1}{{11}}\Omega \)
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