Battery
$\displaystyle \small \bullet$ Battery is used to convert the chemical energy into electrical energy (DC).
$\displaystyle \small \bullet$ Battery is a combination of many electrical cells. These cells are arranged either in series, parallel or combination of both according to the requirement.
Internal Resistance of the Cell
When a current is passed through a cell, the resistance offered to the flow of current is known as internal resistance of the cell.
$\displaystyle \small r=\frac{E-IR}{I}$
where,
r = internal resistance in Ohms
E = electromotive force of the cell in Volt
I = circuit current in Ampere
R = load resistance in Ohms
Connection of Cells
Series Connection
$\displaystyle \small \bullet$ To obtain greater electromotive force, the cells are connected in series.
$\displaystyle \small \bullet$ One end of a cell (-) is connected to the other end (+)
Total electromotive force, $\displaystyle \small E_{T}=n.E$ Volts
Total internal resistance, $\displaystyle \small r_{T}=n.r$ Ohms
Circuit current, $\displaystyle \small I=\frac{V}{I}=\frac{E_{T}}{r_{T}+R}$ Ampere
where,
E = electromotive force of a cell in Volts
$\displaystyle \small E_{T}$ = total electromotive force of all the cells in Volts
r = internal resistance of a cell in Ohms
$\displaystyle \small r_{T}$ = total internal resistance in Ohms
R = load resistance in Ohms
n = number of cells in the combination
I = current in the circuit in Ampere
Parallel Connection
$\displaystyle \small \bullet$ To obtain greater magnitude of electromotive force and continuous supply of electricity for longer period of time, the cells are connected in parallel.
$\displaystyle \small \bullet$ All (-) are connected on one side and all (+) are connected on the same side.
Total electromotive force, $\displaystyle \small E_{T}=E$ Volts
Total internal resistance, $\displaystyle \small r_{T}=\frac{r}{n}$ Ohms
Circuit current, $\displaystyle \small I=\frac{V}{I}=\frac{nE}{r+nR}$ Ampere
Mixed Connection
$\displaystyle \small \bullet$ To obtain grater amount of electromotive force along with current for longer period of time, certain cells are connected in series and this combination is connected in parallel.
$\displaystyle \small \bullet$ In mixed connection, if every branch contains (n) cells and there are (m) such branches, then total number of cells in the connection is given by $\displaystyle \small N=n.m$
Electromotive force of each branch = n.E
Total electromotive force in the circuit, $\displaystyle \small E_{T}=n.E$
Internal resistance for each branch = n.r
Total internal resistance of circuit, $\displaystyle \small r_{T}=\frac{n.r}{m}$
Total current in the circuit, $\displaystyle \small I=\frac{nE}{\frac{nr}{m}+R}$
Maximum current = number of series connected branches arranged parallel ✕ load resistance = number of cells in a series in one branch ✕ internal resistance of a cell
$\displaystyle \small m.R=n.r$
Battery Charging
$\displaystyle \small \bullet$ Chemical energy is stored in the battery.
$\displaystyle \small \bullet$ Current supply in the battery is Direct current (DC).
$\displaystyle \small \bullet$ When battery is connected to the electric supply, during the process of charging, electric energy gets transformed into chemical energy.
$\displaystyle \small \bullet$ When battery is connected to load, this chemical energy gets converted into electric energy and is supplied to various machines.
$\displaystyle \small \bullet$ This chemical reaction is reversible in the case of secondary cells.
Let us assume,
$\displaystyle \small I_{c}$ = charging current in Ampere
$\displaystyle \small T_{c}$ = charging time in hours
$\displaystyle \small V_{c}$ = charging voltage in Volts
$\displaystyle \small I_{d}$ = discharging current in Ampere
$\displaystyle \small T_{d}$ = discharging time in hours
$\displaystyle \small V_{d}$ = discharging voltage in Volts
Charging current while charging the battery,
Efficiency of battery
Ampere-hour Efficiency
Watt-hour Efficiency
[For lead acid battery, $\displaystyle \small \eta _{AH}$ ranges from 90% to 95% and magnitude of $\displaystyle \small \eta _{WH}$ varies from 80% to 85%]
Energy in the form of heat = $\displaystyle \small (charging \; current)^{2}$ $\displaystyle \small \times total\; resistance$ $\displaystyle \small \times charging\; time$
where,
$\displaystyle \small input\; energy=V_{c}.I_{c}.T_{c}$
$\displaystyle \small \bullet$ Battery is used to convert the chemical energy into electrical energy (DC).
$\displaystyle \small \bullet$ Battery is a combination of many electrical cells. These cells are arranged either in series, parallel or combination of both according to the requirement.
Internal Resistance of the Cell
When a current is passed through a cell, the resistance offered to the flow of current is known as internal resistance of the cell.
$\displaystyle \small r=\frac{E-IR}{I}$
where,
r = internal resistance in Ohms
E = electromotive force of the cell in Volt
I = circuit current in Ampere
R = load resistance in Ohms
Connection of Cells
Series Connection
$\displaystyle \small \bullet$ To obtain greater electromotive force, the cells are connected in series.
$\displaystyle \small \bullet$ One end of a cell (-) is connected to the other end (+)
Total electromotive force, $\displaystyle \small E_{T}=n.E$ Volts
Total internal resistance, $\displaystyle \small r_{T}=n.r$ Ohms
Circuit current, $\displaystyle \small I=\frac{V}{I}=\frac{E_{T}}{r_{T}+R}$ Ampere
where,
E = electromotive force of a cell in Volts
$\displaystyle \small E_{T}$ = total electromotive force of all the cells in Volts
r = internal resistance of a cell in Ohms
$\displaystyle \small r_{T}$ = total internal resistance in Ohms
R = load resistance in Ohms
n = number of cells in the combination
I = current in the circuit in Ampere
Parallel Connection
$\displaystyle \small \bullet$ To obtain greater magnitude of electromotive force and continuous supply of electricity for longer period of time, the cells are connected in parallel.
$\displaystyle \small \bullet$ All (-) are connected on one side and all (+) are connected on the same side.
Total internal resistance, $\displaystyle \small r_{T}=\frac{r}{n}$ Ohms
Circuit current, $\displaystyle \small I=\frac{V}{I}=\frac{nE}{r+nR}$ Ampere
Mixed Connection
$\displaystyle \small \bullet$ To obtain grater amount of electromotive force along with current for longer period of time, certain cells are connected in series and this combination is connected in parallel.
$\displaystyle \small \bullet$ In mixed connection, if every branch contains (n) cells and there are (m) such branches, then total number of cells in the connection is given by $\displaystyle \small N=n.m$
Total electromotive force in the circuit, $\displaystyle \small E_{T}=n.E$
Internal resistance for each branch = n.r
Total internal resistance of circuit, $\displaystyle \small r_{T}=\frac{n.r}{m}$
Total current in the circuit, $\displaystyle \small I=\frac{nE}{\frac{nr}{m}+R}$
Maximum current = number of series connected branches arranged parallel ✕ load resistance = number of cells in a series in one branch ✕ internal resistance of a cell
$\displaystyle \small m.R=n.r$
Battery Charging
$\displaystyle \small \bullet$ Chemical energy is stored in the battery.
$\displaystyle \small \bullet$ Current supply in the battery is Direct current (DC).
$\displaystyle \small \bullet$ When battery is connected to the electric supply, during the process of charging, electric energy gets transformed into chemical energy.
$\displaystyle \small \bullet$ When battery is connected to load, this chemical energy gets converted into electric energy and is supplied to various machines.
$\displaystyle \small \bullet$ This chemical reaction is reversible in the case of secondary cells.
Let us assume,
$\displaystyle \small I_{c}$ = charging current in Ampere
$\displaystyle \small T_{c}$ = charging time in hours
$\displaystyle \small V_{c}$ = charging voltage in Volts
$\displaystyle \small I_{d}$ = discharging current in Ampere
$\displaystyle \small T_{d}$ = discharging time in hours
$\displaystyle \small V_{d}$ = discharging voltage in Volts
Charging current while charging the battery,
Efficiency of battery
Ampere-hour Efficiency
Energy in the form of heat = $\displaystyle \small (charging \; current)^{2}$ $\displaystyle \small \times total\; resistance$ $\displaystyle \small \times charging\; time$
$\displaystyle \small input\; energy=V_{c}.I_{c}.T_{c}$
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