# Internal Resistance of a Cell – Know the Definition, Formula and Equation

It is crucial to prepare this Physics topic on the Internal Resistance of a Cell if you are preparing to appear for the Engineering Entrance Exams such as JEE Main and BITSAT. Read this article about the Internal Resistance of a Cell and learn about the related formula for internal resistance of a cell and much more! Also, check relevant diagrams and FAQs related to the Internal resistance of the cell to get an idea about the kind of questions asked in the exam.

**Internal Resistance of a Cell**

A cell has two terminals; positive and negative terminal. The positive terminal is known as the cathode and the negative terminal is known as the anode. They both are the electrodes of a cell. Two or more cells combine together serially or parallelly to form a battery.

The terminal of the cell is connected with a wire to make a closed circuit. Electric current flows from the positive terminal of cell to negative terminal through the wire and at the same time positive ions in the electrolyte flow from lower to higher potential due to which some resistance is offered to the current flow.

**Define Internal Resistance**

It is the resistance (opposing force) in the flow of current when the circuit gets because of electrolyte and electrodes present in the battery/cell.

- It is present within the cell or battery.
- Measures in ohm.
- Fresh/new cell has low internal resistance but increases with continuous use.
- Potential drops across the terminal as the current flows.

**Internal Resistance of a Cell Depends on**:

- Nature of the electrolyte of the cell.
- Directly proportional to the concentration of electrolyte.
- Inversely proportional to the area of electrodes (anode and cathode) in an electrolyte.
- Inversely proportional to the temperature.
- Directly proportional to the distance between cathode and anode (electrodes).

**Emf (Electromotive Force) of a Dry Cell**

Electromotive Force: It is the energy provided by the cell per unit charge (coulomb) that passes through it. It is the potential difference developed across the two terminals of a battery in an open circuit.

In an open circuit, I = 0 (no current flows) i.e. V(open)= EMF

- Lechlanche cell is considered a dry cell and its EMF ranges from 1.2 to 1.5 V.
- EMF is always greater than or equal to V (potential difference).
- EMF of a cell,

**Formula for Internal Resistance of a Cell **

ℰ: emf of a cell (in volts)

V: Potential difference across a cell (in Volts)

I: Current flowing through a conductor( in Ampere)

r: Internal Resistance (in ohm)

R: External resistance (in ohm)

We know that,

**Emf** is the work done by the cell to carry a unit charge through the closed circuit. So, it is the sum of the work done to carry the charge through the conducting wire with external resistance(R) and cell with internal resistance (r).

ℰ = V+V’ ——————–(1)

By Ohms Law

V=IR ———— (2)

V’ =Ir ————–(3)

From equation (2) and (3)

ℰ = IR + Ir

v = I (r + R)

I=ℰ /(R+r) ———————(4)

Substituting (4) in (2)

V= IR = (Rℰ)/(R+r)

Now, from equation (1)

V= ℰ – V’

= ℰ – Ir

Ir = ℰ – V

r = (ℰ -V) / I

putting I=V/R

r =(ℰ -V)R / I

**Calculate Emf of a Cell**

**A- emf of cells are connected in series.**

- The negative terminal of the cell, connected to the positive terminal of another cell and, they are said to be connected in series. The potential difference will be different across each cell and the current will be the same.

**Equivalent emf of the cell in series**

ℰ_{eq}=ℰ_{1}+ℰ_{2}+ℰ_{3}+………..+ℰ_{n }

**Equivalent Internal resistance of cell in series**

r_{eq}= r_{1}+r_{2}+r_{3}+r_{4}+…………..+r_{n }

- If any of the cells are connected in the opposite direction i.e. positive terminal of one cell (ℰ
_{1}) is connected to the positive terminal of another cell(ℰ_{2}).

**Equivalent emf of cells in series**

ℰ_{eq}=ℰ_{1}-ℰ_{2}+ℰ_{3}+………..+ℰ_{n }

**B- If the cells are connected in parallel**

The positive terminal of all the cells is connected to a single point and also the negative terminal of those cells is connected to one point.

The potential difference remains the same for all the cells connected in parallel but Current flowing through them is different.

**Equivalent emf of cells connected parallel**

** **

**Equivalent Internal Resistance of cells in parallel**

So, this is all about the Internal Resistance of a Cell. Get some practice of the same on our free Testbook App. Download Now!

**Internal Resistance of a Cell FAQ’S**

**Q.1**

**Can internal resistance of a battery change?****Ans.1**

Yes, the internal resistance of a battery increases when we continuously draw current across it. New battery or cell has low internal resistance.

**Q.2**

**What is the SI unit of emf?****Ans.2**

As we know that emf is the energy that drives electric charge through the circuit. It is provided by battery or cell. So emf is measured in Volt(V).

**Q.3**

**Why internal resistance does not remain constant?****Ans.3**

As the battery or cell is in continuous use, consuming electrolyte and the chemical reaction keeps occurring in the cell, due to which the concentration of ions in the cell decreases and this resists the flow of charge through it. Hence, the internal resistance increases with time.

**Q.4**

**How can we differentiate between emf and Potential Difference?****Ans.4**

- The main difference between the potential difference and emf is that emf exists in the circuit, even when it is not closed whereas potential difference occurs when the circuit is closed.
- Emf is a cause but the potential difference is an effect.
- The emf is not dependent on external resistance of a circuit, while the potential difference is always less than emf.

**Que 5.** **Find the current drawn from a cell of emf 1V and internal resistance ⅔ Ω connected to the network given below?**

** Solution:**

Clearly the above circuit diagram can be redrawn as follows:

Given,

r (internal Resistance) = ⅔ Ω

ℰ = 1V