Three resistors of equal resistance R are connected in series and then connected in parallel. What will be the ratio of equivalent resistance in series and parallel?

  1. 1 : 9
  2. 1 : 3
  3. 3 : 1
  4. 9 : 1

Answer (Detailed Solution Below)

Option 4 : 9 : 1
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Detailed Solution

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CONCEPT:

  • Resistance: The obstruction offered to the flow of current is known as the resistance. It is denoted by R.
  • When two or more resistances are connected one after another such that the same current flows through them then it is called resistances in series.
  • The equivalent resistance in series combination is will be

 

Rser = R1 + R2 + R3

F1 Jitendra Deepak 30.03.2020 D7

  • When the terminals of two or more resistances are connected at the same two points and the potential difference across them is equal then it is called resistances in parallel.

 

F1 Jitendra Deepak 30.03.2020 D8

  • 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:

Given that,

R1 = R2 = R3 = R

When resistor are connected in series, then the equivalent resistance is

Rser = R1 + R2 + R3 = R + R + R = 3R       ---(1)

When the resistor is connected in parallel, then the equivalent resistance is

\(\frac{1}{{{R_{para}}}} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}} + \frac{1}{{{R_2}}} = \frac{1}{R} + \frac{1}{R} + \frac{1}{R} = \frac{3}{R}\)

∴ Rpara = R/3       ---(2)

Divide equation 1 and 2, we get

\(\frac{{{R_{ser}}}}{{{R_{para}}}} = \frac{{3R}}{{\frac{R}{3}}} = 9:1\)

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