Answer

Verified

341.1k+ views

**Hint:**The word “equivalent” means the total. To derive the expression for effective resistance in the parallel combination of the two resistors, draw the circuit diagram of the two resistors connected parallel to each other. Use Kirchhoff’s current law to express the current at the junction to derive the expression.

**Complete step by step answer:**

Equivalent resistance is nothing but the total resistance in the circuit. If we connect the number of resistors one after another to the same wire, the total resistance of the wire increases because the resistance of each resistor adds up. Also, when we connect the number of resistors parallel to each other, the total resistance of the circuit decreases. Thus, we can say that the equivalent resistance is the resistance encountered by the whole circuit.Let the two resistors are connected in parallel combination as shown in the figure below.

We know that the voltage in the parallel arm remains the same. Therefore, the voltage across the resistor \[{R_1}\] and the voltage across the resistor \[{R_2}\] is the same.Applying Kirchhoff’s current law at the junction A in the above circuit, we get,

\[I = {I_1} + {I_2}\]

Using Ohm’s law, we can write the above equation as,

\[\dfrac{V}{{{R_{eff}}}} = \dfrac{V}{{{R_1}}} + \dfrac{V}{{{R_2}}}\]

Here, \[{R_{eff}}\] is the effective resistance of the two resistors and V is the voltage which is the same across the two resistors.

Simplifying the above equation, we get,

\[\dfrac{1}{{{R_{eff}}}} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}}\]

\[ \therefore {R_{eff}} = \dfrac{{{R_1}{R_2}}}{{{R_1} + {R_2}}}\]

This is the required expression for the effective resistance of the two resistors connected parallel to each other.

**Note:**Students can also derive the expression for effective resistance in the series combination of the two resistors in the same manner as we have done in the above section. Remember, the current remains the same in series combination and the voltage remains the same in parallel combination. This is the key to derive the expression for both effective resistances in the series combination and the parallel combination. Also, students should remember KVL and KCL.

Recently Updated Pages

Basicity of sulphurous acid and sulphuric acid are

The branch of science which deals with nature and natural class 10 physics CBSE

Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred

What is the stopping potential when the metal with class 12 physics JEE_Main

The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main

How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Distinguish between the reserved forests and protected class 10 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give simple chemical tests to distinguish between the class 12 chemistry CBSE

Difference Between Plant Cell and Animal Cell

Which of the following books is not written by Harshavardhana class 6 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

In which states of India are mango showers common What class 9 social science CBSE

What Made Mr Keesing Allow Anne to Talk in Class class 10 english CBSE