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CBSE Class 12-science Answered

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.

Asked by my3shyll | 24 Sep, 2018, 07:33: PM
Expert Answer
 
                                     (1) 
 
Applying to Kirchoff's voltage law,
 
For loop A-B-D-E-A we get,
 
-RI -10I + 10 = 0
 
→ 10 = RI +10I ...(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),
 
             RI +10I1       = 10
- ]      10I1 - 10I- 2 IR = 4
         (-)    (+)    (+)         
           3RI + 10 I = 6      ...(5)
 
Equation (5) can be written as, 
2 space equals space I R space plus space 10 over 3 I space
rightwards double arrow space 2 space equals open parentheses space R space plus space 10 over 3 close parentheses space I space... left parenthesis 6 right parenthesis
 
By Ohm's law,
Veff= I (R + Reff)
 Comparing thios equation with (6),
 
Veff= 2 Volt and Reff = 10/3 = 3.33 Ω
 
The equivalent circuit for figure (1) is,
 
 

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