The reaction which is taking place in a nickel-cadmium battery can be represented by which of the following equations?
A) ${\text{Cd}} + {\text{Ni}}{{\text{O}}_2} + 2{{\text{H}}_2}{\text{O}} \to {\text{Cd}}{\left( {{\text{OH}}} \right)_2} + {\text{Ni}}{\left( {{\text{OH}}} \right)_2}$
B) ${\text{Cd}} + {\text{Ni}}{{\text{O}}_2} + 2{\text{O}}{{\text{H}}^ - } \to {\text{Ni}} + {\text{Cd}}{\left( {{\text{OH}}} \right)_2}$
C) ${\text{Ni}} + {\text{Cd}}{\left( {{\text{OH}}} \right)_2} \to {\text{Cd}} + {\text{Ni}}{\left( {{\text{OH}}} \right)_2}$
D) \[{\text{Ni}}{\left( {{\text{OH}}} \right)_2} + {\text{Cd}}{\left( {{\text{OH}}} \right)_2} \to {\text{Ni}} + {\text{Cd}} + 2{{\text{H}}_2}{\text{O}}\]

Hint:Nickel-cadmium batteries is a rechargeable battery. Nickel-cadmium batteries are made up of nickel-oxide hydroxide and metallic cadmium as electrodes. To solve this we must know the reactions occurring at anode and cathode in the nickel cadmium battery.

Complete step-by-step answer:
We know that the nickel-cadmium battery is made up of nickel oxide hydroxide and metallic cadmium as electrodes.The nickel-cadmium battery contains a nickel oxide-hydroxide electrode, cadmium electrode, separator and an alkaline electrolyte. The anode i.e. the negative electrode is made up of cadmium metal while the cathode i.e. the positive electrode is made up of nickel oxide hydroxide.

The reactions involved in nickel-cadmium battery are as follows:
At anode: ${\text{Cd}} + 2{\text{O}}{{\text{H}}^ - } \to {\text{Cd}}{\left( {{\text{OH}}} \right)_2} + 2{{\text{e}}^ - }$
At cathode: ${\text{Ni}}{{\text{O}}_2} + 2{{\text{H}}_2}{\text{O}} + {\text{2}}{{\text{e}}^ - } \to {\text{Ni}}{\left( {{\text{OH}}} \right)_2} + 2{\text{O}}{{\text{H}}^ - }$
Overall reaction: ${\text{Cd}} + {\text{Ni}}{{\text{O}}_2} + 2{{\text{H}}_2}{\text{O}} \to {\text{Cd}}{\left( {{\text{OH}}} \right)_2} + {\text{Ni}}{\left( {{\text{OH}}} \right)_2}$
When a nickel-cadmium battery is recharged, the reaction goes from right to left. The alkaline electrolyte used in the battery is not consumed in the reaction.
Nickel-cadmium batteries can supply high current due to their low internal resistance and good current conducting properties. Nickel-cadmium batteries can supply extremely high currents. Also, they can be rapidly recharged.
Thus, the reaction taking place in nickel-cadmium battery can be represented by is ${\text{Cd}} + {\text{Ni}}{{\text{O}}_2} + 2{{\text{H}}_2}{\text{O}} \to {\text{Cd}}{\left( {{\text{OH}}} \right)_2} + {\text{Ni}}{\left( {{\text{OH}}} \right)_2}$.
Thus, the correct option is (A) ${\text{Cd}} + {\text{Ni}}{{\text{O}}_2} + 2{{\text{H}}_2}{\text{O}} \to {\text{Cd}}{\left( {{\text{OH}}} \right)_2} + {\text{Ni}}{\left( {{\text{OH}}} \right)_2}$.

Note: Nickel-cadmium batteries are used in cordless and wireless telephones, emergency lighting and other applications. Nickel-cadmium batteries are also used as a substitute for primary cell, aircraft batteries, electric vehicle batteries and stand by power uses. The cadmium in these batteries is a heavy metal and is toxic. Thus, disposal of nickel-cadmium batteries requires special care.