The very oddly drawn circuit above I tried consists of two f

The very oddly drawn circuit above (I tried) consists of two flashlight batteries and two Nichrome wires of different lengths and different thicknesses. The thin wire is 49cm long, and its diameter is 0.25mm. The thick wire is 15cm long, and its diameter is 0.34mm. If the emf of each flashlight battery is 1.5 volts, determine the steady state electric field inside the thin wire. Remember, you need to satisfy both the current node rule (conservation of charge) along with conservation of energy. 5.25 V/m 0 V/m 2.84 V/m 10.5 V/m

Solution

Suppose resistivity of nichrome wire is rho.

and R = rho * L / A

for thin wire:

R1 = rho * (49 cm ) / (pi * (0.25/2)^2)

R1 = k (49/0.25^2) = 784k

where k is constant.

for thick wire:

R2 = k (15 / 0.34^2) = 130k

R1 and R2 are connected in series.

and PD across (R1 + R2) = 2 x 1.5 = 3 volt

PD across thin wire = 3 x R1 / (R1 + R2)

         = 2.57 Volt

and E = V/d = (2.57) / (0.49) = 5.25 V/m