Two cells of voltage 10 v and 2 v and internal resistances of 10ohm and 5 ohm respectively, are connected in parallel with positive end of 10v battery connected to negative pole of 2v battery.find the effective voltage and effective internal resistance of the combination.
(1)
Applying to Kirchoff’s voltage law,
For loop A-B-D-E-A we get,
-RI -10I + 10 = 0
→ 10 = RI +10I1 …(1)
Applying Kirchoff’s voltage law for loop F-A-B-C-F,
-2 - RI + 5 I2 = 0
→5 I2 - RI = 2 …(2)
We know,
by Kirchoff’s current law,
I1 = I + I2
→ I2 = I1 - I
Substituting it in equation (2),
5 (I1 - I) - RI = 2 … (3)
multiplying equation (3) by ‘2’
10I1- 10I- 2 IR = 4 …(4)
Subtracting equation (4) from (1),
Equation (5) can be written as,
By Ohm’s law,
V eff= I (R + R eff)
Comparing thios equation with (6),
V eff= 2 Volt and R eff = 10/3 = 3.33 Ω
The equivalent circuit for figure (1) is,
