Internal Resistance: Batteries & Voltage Sources

• Internal resistance is the opposition to the flow of current within a battery or other voltage source
• It's the resistance within the source itself, not an external load
• It's denoted by 'r' and is in series with the ideal voltage source

Origin of Internal Resistance

• In batteries, internal resistance arises from the electrolyte, electrodes, and separators
• The electrolyte's conductivity limits ion flow, contributing to resistance
• Electrode material and surface area affect the ease of electron transfer, influencing resistance
• Separators impede ion flow, adding to internal resistance
• In power supplies, components like transformers, rectifiers, and internal wiring contribute

Effects of Internal Resistance

• Internal resistance reduces the terminal voltage of a source when delivering current
• The voltage drop across the internal resistance is proportional to the current (V = Ir)
• Higher internal resistance leads to a greater voltage drop for the same current
• Internal resistance causes power dissipation within the source as heat (P = I^2r)
• This reduces the efficiency of the voltage source, wasting energy

Impact on Circuit Performance

• Internal resistance limits the maximum current a voltage source can deliver
• The maximum current occurs when the terminals are short-circuited (I = E / r, where E is the source voltage)
• It affects the voltage regulation of a source (its ability to maintain a constant voltage under varying load)
• A higher internal resistance leads to poorer voltage regulation
• It influences the damping of transient responses in circuits
• It can cause voltage sag when a sudden load is applied
• Internal resistance can affect the matching of a source to a load for maximum power transfer

Factors Affecting Internal Resistance

• Temperature can affect internal resistance
• In batteries, lower temperatures generally increase internal resistance
• Battery chemistry influences internal resistance
• Different battery types (e.g., lead-acid, lithium-ion) have different internal resistances
• The state of charge of a battery affects its internal resistance
• Internal resistance increases as the battery discharges

Measuring Internal Resistance

• Open-circuit Voltage Method involves measuring the open-circuit voltage (Voc) and short-circuit current (Isc)
• The internal resistance is then calculated as r = Voc / Isc
• Load Method measures the terminal voltage under two different load conditions
• r = (V1 - V2) / (I2 - I1), where V1 and I1 are voltage and current at one load, and V2 and I2 at another
• AC Impedance Spectroscopy applies a small AC signal to the source and measures the impedance
• It provides more detailed information about the frequency-dependent behavior of the internal resistance

Internal Resistance in Batteries

• It increases with age due to chemical changes and electrode degradation
• It affects battery performance, including discharge rate and energy delivery
• It can be an indicator of battery health
• Monitoring internal resistance can help detect battery degradation or failure
• Lower internal resistance is generally desirable in most battery applications

Internal Resistance in Solar Cells

• It is a critical parameter affecting solar cell efficiency
• Series resistance (RS) is a component of internal resistance, arising from contacts and semiconductor material
• Shunt resistance (RSH) is another component, representing leakage current paths across the cell
• High series resistance and low shunt resistance reduce cell performance
• Internal resistance reduces the fill factor of the solar cell's I-V curve

Minimizing Internal Resistance

• Use materials with high conductivity for electrodes and connections
• Optimize electrolyte composition and concentration
• Reduce the distance between electrodes
• Increase the surface area of electrodes to lower current density
• Employ designs that minimize contact resistance
• Control temperature to maintain optimal operating conditions

Internal Conductance

• Internal conductance ('g') is the reciprocal of internal resistance (g = 1/r)
• It represents the ease with which current flows within the source
• It can be used in circuit models as a parallel element to the ideal voltage source
• Higher internal conductance corresponds to lower internal resistance

Modeling Internal Resistance

• In circuit analysis, a voltage source with internal resistance is modeled as an ideal voltage source in series with a resistor 'r'
• This model accurately predicts the behavior of the source under various load conditions
• Thevenin's theorem can be used to simplify circuits with voltage sources and internal resistance
• Norton's theorem provides an equivalent current source representation with a parallel internal resistance

Applications

• Power supplies should have low internal resistance to maintain stable output voltage
• Batteries for high-drain devices (e.g., power tools) need low internal resistance for high current delivery
• Solar cells require minimized internal resistance to maximize power output
• Supercapacitors benefit from low internal resistance for fast charging and discharging
• Audio amplifiers need low output impedance (equivalent to low internal resistance) to drive speakers effectively

Alternative Terminology

• Source impedance is sometimes used interchangeably with internal resistance, especially in AC circuits
• Output impedance is the equivalent impedance looking back into the output terminals of a circuit
• Series resistance specifically refers to resistive elements in series with the voltage source within the device

Explore internal resistance in voltage sources. Internal resistance opposes current flow within a battery. It stems from electrolytes and electrodes, reducing terminal voltage when current is drawn.