Charging Of Battery And Discharging Of Battery

Emf of a Cell When the Cell is Charging and Discharging

Before moving to the charging and discharging, will study open and closed circuits.

What is an Open Circuit?

No current is taken from the cell. $i=0$
The potential difference between $\mathrm{A}$ and $\mathrm{B}{V}_{AB}=E$
The potential difference between $\mathrm{C}$ and $\mathrm{D}{V}_{CD}=0$

What is a Short Circuit?

Two terminals of a cell are joined together by a thick conducting wire then,

Maximum current -

$\begin{array}{rl}& i=\frac{E}{r}\\ & V=0\end{array}$

Equation of Cell

1. When supplying the current: $E=V+iR$
2. When the cell is being charged: $E=V-iR$

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Solved Examples Based on Charging of Battery And Discharging of Battery

Example 1: The length of a wire of a potentiometer is 100 cm and the e.m.f. of its standard cell is E volt. It is employed to measure the e.m.f. of a battery whose internal resistance is 0.5 $\Omega$ If the balance point is obtained at $l=30$ cm from the positive end, the e.m.f. of the battery is :

1) $\frac{30E}{100.5}$
2) $\frac{30E}{100-0.5}$
3) $\frac{30E}{100}-0.5i$
4) $\frac{30E}{100}$

Solution:

Using the principle of potentiometer

i.e $V\propto l$ $\frac{V}{E}=\frac{l}{L}$ or $V=\frac{l}{L}E=\frac{30E}{100}$

Hence, the answer is option (4).

Example 2: In the given circuit value of current (in A) through the circuit when the switch is open is

1) 0

2) 2

3) 1

4) 4

Solution:

Current through the circuit

i=0

wherein

No current will pass through the resistor

Example 3: The potential difference between points A and B in the given circuit is

1) $V_{AB}=E$
2) $V_{AB}=0$
3) $V_{AB}>E$
4) $V_{AB}<E$

Solution:

As we learntPotential difference between $A$ and $B$
$V_{AB}=E$

wherein

$\mathrm{I}=0$
P.D. across the resistor is zero.
$V_{AB}=E$

Hence, the answer is option (1).

Example 4: In the given figure current (in A) passing through $5\mathrm{\Omega }$ resistor is:

1) 0

2) 2

3) 2.5

4) 5

Solution:

Short circuit -Two terminals of a cell are joined together by a thick conducting wire

Since $10\mathrm{\Omega }$ is short-circuited hence no current will pass through $10\mathrm{\Omega }$ and $5\mathrm{\Omega }$
So,
$\mathrm{I}=0\mathrm{A}$

Example 5: If the terminal of a battery is short-circuited then the current flowing through it is:

1) zero

2) minimum

3) maximum

4) none of the above

Solution:

When a battery is short-circuited, the terminal voltage is zero. The current passing through the cell is the maximum.

Hence, the answer is option (3).

Summary

Supplying electrical energy to a battery for it to store energy for later use is called charging. The battery receives the input of electricity causing an electrical current to flow through it hence energy is stored in its cells through some chemical reactions. Discharging a battery occurs when one is using it to power a device or an appliance. The device is powered by electrical energy which is changed from the stored chemical energy.