Question

How is the internal resistance of a voltage source taken into account in circuit analysis?

Answer 1

In circuit analysis, the internal resistance of a voltage source is often taken into account by considering it as a series resistor connected in series with the ideal voltage source. This internal resistance represents the inherent resistance of the source due to the physical properties of the source's components (e.g., batteries, power supplies, etc.).

Let's assume you have an ideal voltage source, V_source, with an internal resistance, R_internal. When analyzing a circuit, you model this voltage source as follows:

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   + ----------[ R_internal ]---------- +
   |                                  |
----                                ----
   |                                  |
   |                                  |
   V_source                           Load


Here:

The '+' and '-' signs represent the positive and negative terminals of the voltage source, respectively.
R_internal is the internal resistance of the voltage source.
The 'Load' represents the rest of the circuit connected to the voltage source.

When analyzing the circuit, you can now take into account the internal resistance in the following ways:

Voltage Division:
When current flows through the internal resistance, it causes a voltage drop across it. So, the voltage across the load will be reduced due to the internal resistance. The voltage across the load, V_load, can be calculated using voltage division:

V_load = V_source * (R_load / (R_load + R_internal))

Here, R_load is the resistance of the load connected to the voltage source.

Current Division:
The internal resistance causes some of the current supplied by the voltage source to flow through it. The current flowing through the load, I_load, can be calculated using current division:

I_load = I_source * (R_internal / (R_load + R_internal))

Here, I_source is the current supplied by the voltage source.

Maximum Power Transfer:
When the load resistance, R_load, is equal to the internal resistance, R_internal, the circuit reaches maximum power transfer. In this case, half of the power is dissipated in the internal resistance, and the other half in the load resistance. The formula for maximum power transfer is:

P_max = (V_source^2) / (4 * R_internal)

By taking into account the internal resistance in the circuit analysis, you can get more accurate results and understand the impact of the source's internal characteristics on the overall circuit behavior.