Understanding Nodal Analysis: How Voltage at Node D is Calculated

[Nyasha]

Guys l would like to know how does the the voltage at node D become :

Vd=-(Vc-Va)=Va-Vc

 

[The Electrician]

Calculate ix = (VC-VA)/2. You see why this is, I hope. Ask if you don't.

Then the dependent source feeding VD has a voltage VD =-2*ix. Substituting what we calculated for ix above, we have VD = -2*ix = -2*(VC-VA)/2 = VA-VC.

 

[Mene]

Nodal analysis is a method used in circuit analysis to determine the voltage and current at different nodes in a circuit. In this particular case, we are interested in finding the voltage at node D.

To understand how the voltage at node D is calculated, we need to first understand the concept of Kirchhoff's Voltage Law (KVL). KVL states that the sum of all voltages around a closed loop in a circuit is equal to zero. In other words, the total voltage drop across a closed loop in a circuit must be equal to the total voltage rise.

Now, let's apply this concept to the circuit in question. We have two voltage sources, Vc and Va, connected in series with a resistor. The voltage at node D is the voltage drop across this resistor. Using KVL, we can write the following equation:

Vc + Vd + Va = 0

Since Vc and Va are connected in series, their voltages will be equal. Therefore, we can rewrite the equation as:

Vc + Vd + Vc = 0

Simplifying, we get:

Vd = -Vc

This equation tells us that the voltage at node D is equal to the negative of the voltage at node C. However, in order to find the actual voltage at node D, we need to know the voltage at node C. This is where the second part of the equation comes in.

We know that the voltage at node C is equal to the voltage drop across the resistor, which is given by Ohm's Law:

Vc = I*R

Substituting this into our previous equation, we get:

Vd = -I*R

Finally, we can use the relationship between voltage and current in a resistor, V = I*R, to rewrite the equation as:

Vd = -(Vc - Va) = Va - Vc

This equation gives us the final result, which tells us that the voltage at node D is equal to the difference between the voltages at nodes C and A. In other words, the voltage at node D can be calculated by subtracting the voltage at node C from the voltage at node A.

In summary, the voltage at node D is calculated using Kirchhoff's Voltage Law, Ohm's Law, and the relationship between voltage and current in a resistor. This method, known as nodal analysis, is a powerful tool for understanding and analyzing circuits.