Question

Draw diagram showing resistors in series. Explain the changes in potential difference and electric current. Apply Ohm's law write the related equations

Answer 1

The diagram of resistors in series is given in the attachment.

• Three resistors R1, R2 and R3 are connected in series across a dc voltage supply V and a current I flows in the circuit.
• Since, the three resistors are connected in series, the electric current I flowing through all of them is the same, equal to I.
• But, due to the series connection, the potential difference across each resistor will vary, depending upon the value of their resistances.
• By Ohm's law, the voltage drop across the resistance is given by -

                                                         V1 = IR1

                                                         V2 = IR2

                                                         V3 = IR3

Where, V1, V2 and V3 are the voltage drop across the respective restors.

• Now, finding the quivalent resistance of the circuit across V,

                                                 Req = R1 + R2 + R3

• Total current I flowing through the circuit is given by

                                           I = V/Req = V/(R1 + R2 + R3)

• Now, substituting the value of I in V1, V2 and V3,

                                   V1 = (V*R1)/(R1 + R2 + R3) = V*R1/Req

                                   V2 = (V*R2)/(R1 + R2 + R3) = V*R1/Req

                                   V3 = (V*R3)/(R1 + R2 + R3) = V*R1/Req

• From the above equations, it is clear that the potential difference across a resistor, connected in series, will increase with increase in its resistance. ( This is because V and Req is constant)