Determine the current in and the potential difference across

Determine the current in and the potential difference across the 9.0 Ohm resistor in the circuit diagram at right.

Solution

8 ohm and 9 ohm are in parallel.

Let the resultnat of these two resistors be R then

(1/R )=(1/8)+(1/9)

   R = (8x9)/(8+9)

      = 72 /17

      = 4.235 ohm

R , 4 ohm ,2 ohm,6 ohm are in series.

So, equivalent resistance of the circuit R \' = R + 4 + 2+ 6

                                                             = 16.235 ohm

Emf of the cell E = 1.5 volt

So, current in the circuit i = E / R \'

                                     = 1.5 / 16.235

                                     = 92.39 x10 ^-3 A

Current through 9 ohm resistor is i \' = i [ 8 /(8+9)]

                                                    =(92.39 x10 ^-3 ) (8/17)

                                                    = 43.47 x10 ^-3 A

Therefore potential difference across 9 ohm resistor = i \' (9 ohm)

                                                                           = (43.47 x10 ^-3 ) x 9

                                                                           = 0.391 volt