Consider the following circuit: Which one of the following is the value of the resistance between points A and B in the circuit given above?
CONCEPT:
Resistance:
- The measurement of opposition of flow of electric current through a conductor is called as resistance of that conductor. It is denoted by R.
There are mainly two ways of the combination of resistances:
1. Resistances in series:
- When two or more resistances are connected one after another such that the same current flows through them is called as resistances in series .
- The net resistance/equivalent resistance (R) of resistances in series is given by:
- Equivalent resistance, R = R 1+ R 2
2. Resistances in parallel:
- When the terminals of two or more resistances are connected at same two points and the potential difference across them is equal is called as resistances in parallel.
- The net resistance/equivalent resistance(R) of resistances in parallel is given by:
- \(\frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}\)
EXPLANATION:
Here resistance 1 and resistance 2 are in parallel combination
Equivalent resistance of 1 and 2 is R12
\(\frac{1}{{{R_{12}}}} = \frac{1}{R} + \frac{1}{R} = \frac{2}{R}\)
R 12 = R/2
Resistance R 12 and Resistance 3 are in series
Equivalent of R 12 and 3 is R 123
R 123 = R 12 + R = 3R/2
Now the resistance R 123 and 4 are in parallel
Net resistance will is Rnet
\(\frac{1}{{{R_{net}}}} = \frac{1}{{{R_{123}}}} + \frac{1}{R} = \frac{2}{{3R}} + \frac{1}{R} = \frac{5}{{3R}}\)
\({R_{net}} = \frac{3}{5}R\)
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