Question

with the help of a circuit diagram,establish the relationship for the equivalent resistance of three resistances connected in series​

Answer 1

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Series is the combination of resistors when they are connected end to end. The same amount of current flows through it, but the Potential difference is different.

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Refer to the attachment...

The same current will flow throughout the circuit whereas the potential difference between any two points is different. From the diagram,

• $\rm{V_A - V_B = V_1}$
• $\rm{V_B - V_C = V_2}$
• $\rm{V_C - V_D = V_3}$

Sum of the potential difference across the resistors should be equal to the supplied voltage,

⇛ $\rm{V = V_1 + V_2 + V_3}$

Let the equivalent resistance be R, and the current flowing be I (same for the circuit). By using ohm's law:

⇛ V = IR

And,

• $\rm{V_1 = IR_1}$
• $\rm{V_2 = IR_2}$
• $\rm{V_3 = IR_3}$

Then,

⇛ $\rm{IR = IR_1 + IR_2 + IR_3}$

Taking I common both sides of the equation,

⇛ $\rm{IR = I(R_1 + R_2 + R_3)}$

⇛ $\rm{R = R_1 + R_2 + R_3}$

Hence, Total resistance or equivalent resistance of the series combination is the all total sum of individual resistances.