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A battery source of 20 V when connected to a load of 19 Ω draws a current of 1 A. What is the value of internal resistance of battery?
1Ω
39Ω
2Ω
0.5Ω
1Ω
The internal resistance of a battery refers to the opposition to current flow offered by the materials and electrolyte within the cell. It acts in series with the Electromotive Force (EMF) of the battery, causing a voltage drop when current is drawn, as described by Kirchhoff's Voltage Law.
The internal resistance of a battery refers to the opposition to current flow offered by the materials and electrolyte within the cell. It acts in series with the Electromotive Force (EMF) of the battery, causing a voltage drop when current is drawn, as described by Kirchhoff's Voltage Law.
E=I(R+r) — Relation between EMF, current, load, and internal resistance
Vterminal=E−I⋅r — Terminal voltage equation
When a battery with EMF E and internal resistance r is connected to a load R, the total circuit resistance is R+r. According to Ohm's Law, the current I is given by I=R+rE. By rearranging this, we find r=IE−R. Substituting the given values E=20 V, I=1 A, and R=19 \Omega, we get r=120−19=1 \Omega.
Internal resistance reduces the effective voltage available at the battery terminals under load.
The power dissipated internally by the battery is Ploss=I2⋅r.
Ideal batteries have zero internal resistance.
Internal resistance acts as a natural current limiter during short circuit scenarios.
Provides a basis for determining battery state of health and efficiency.
Causes heat generation within the battery during discharge.
Reduces the maximum power transfer efficiency from the source to the load.
Battery management systems (BMS).
Analysis of power supply regulation.
Option B (39Ω) is incorrect as it results from misinterpreting the total resistance as internal resistance.
Option C (2Ω) and D (0.5Ω) are derived from incorrect algebraic manipulation of Ohm's Law.
A is correct — The internal resistance is calculated as 1 \Omega using the voltage drop across the load compared to the EMF.
Always remember that for a battery, the terminal voltage is always less than the EMF when current is flowing: V=E−Ir.
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