Question

Q-10 Derive laws of resistance in series so as to explain equivalent resistance of
circuit?​

Answer 1

Answer:

Explanation:

The resistors are connected across two points in the circuit in such a way that the current flowing through each resistor is the same and only one path is available for it to flow, then the resistors are said be connected in series.\In the figure above, three resistors R1​,R2​ and R3​ are connected in series across the points A and B. Hence, the current (I) flowing through each of the resistors is same but the total voltage of the battery is divided.If the voltage drops across V1​,V2​ and V3​ are R1​,R2​ and R3​ respectively then,

V=V1​+V2​+V3​ …………….(i)

Now, if the resistor R instead of these three resistances R1​,R2​ and R3​ is connected in such a way that the current flowing through the circuit remains the same, then R is called equivalent resistance of the circuit.For an equivalent resistor, V=IR…………….(ii)According to Ohm’s law,

R1​ voltage drops across, V1​=IR1​ …………..(iii)

R2​ voltage drops across, V2​=IR2​ …………..(iv)

R3​ voltage drops across, V3​=IR3​ …………..(v)

Adding (iii), (iv) and (v):

V1​+V2​+V3​=IR1​+IR2​+IR3​ ……(vi)Or,

V=IR=I(R1​+R2​+R3​)Or,

R=R1​+R2​+R3​

Thus, in series connection the equivalent resistor R is equal to the sum of all the resistors connected in series.