2011-06-17 Finding the potential at point A in a resistive circuit using KVL.

Find V_A and the current flowing in the 2 kΩ resistor.

Solution

Collapse the resistance network between point A and the potential -10V to get

2 kΩ || (1 kΩ + 1 kΩ)

= 2 kΩ || 2 kΩ

= [ (2*2)/(2+2) ] kΩ

= 1 kΩ

as shown in the picture below.

Let the current I flows from +10 V to -10 V.

KVL;  

-10 V + (1 kΩ)( I ) + (1 kΩ)( I ) = +10 V

( I )(2 kΩ) = 20 V

I = 10 mA

Then we find V_A from one of these approaches.

KVL;

-10 V + (1 kΩ)( 10 mA ) = V_A 

V_A = 0 V   Ans

or

KVL;

+10 V - (1 kΩ)( 10 mA ) =  V_A 

V_A = 0 V   Ans

Finally, we find I flowing through the 2 kΩ resistor in the first picture.

Ohm's law;

I_2 kΩ = [ V_A - (-10 V) ]  / 2 kΩ = [ 0 V + 10 V ] / 2 kΩ = 5 mA  Ans