Goal: To confirm the validity of the Kirchoff's Rules in the analysis of DC circuits.


Diagram 1 shows the circuit for which we must determine the currents through and the voltage across the resistors. Before we analyze it, we must name the points between each circuit element, and choose the directions of the currents through each resistor (Diagram 2). The two loop and one junction equations, then, are:
We solve the equations:
Resistor  Voltage (V) 
10 &Omega  
30 &Omega  
50 &Omega 
V_{BA}(V)  V_{AD}(V)  V_{DC}(V)  V_{CB}(V)  V_{BA}+V_{AD}+V_{DC}+V_{CB}(V) 
V_{CB}(V)  V_{BD}(V)  V_{DC}(V)  V_{CB}+V_{BD}+V_{DC}(V) 
V_{AD}(V)  V_{DB}(V)  V_{BA}(V)  V_{AD}+V_{DB}+V_{BA}(V) 
Resistor  Current (A) 
10 &Omega  
50 &Omega  
30 &Omega 
Simulation Value  Theoretical Value  
I_{1}  
I_{2}  
I_{3} 
I_{1}  I_{2}  I_{3}  I_{1} + I_{3} 