A battery is charged at a potential of $$15\,V$$ for $$8\,h$$ when the current flowing is $$10\,A.$$ The battery on discharge supplies a current of $$5\,A$$ for $$15\,h.$$ The mean terminal voltage during discharge is $$14\,V.$$ The watt-hour efficiency of the battery is
A.
$$82.5\% $$
B.
$$80\% $$
C.
$$90\% $$
D.
$$87.5\% $$
Answer :
$$87.5\% $$
Solution :
Input energy when the battery is charged
$$\eqalign{
& {E_{{\text{in}}}} = V\,it \cr
& = 15 \times 10 \times 8 \cr
& = 1200\,Wh \cr} $$
Energy released when the battery is discharged
$$\eqalign{
& {E_{{\text{out}}}} = 14 \times 5 \times 15 \cr
& = 1050\,Wh \cr} $$
Hence, watt hour efficiency of battery is given by
$$\eqalign{
& = \frac{{{\text{Energy output}}}}{{{\text{Energy input}}}} = \frac{{1050}}{{1200}} \cr
& = 0.875 = 87.5\% \cr} $$
Releted MCQ Question on Electrostatics and Magnetism >> Electric Current
Releted Question 1
The temperature coefficient of resistance of a wire is 0.00125 per $$^ \circ C$$ At $$300\,K,$$ its resistance is $$1\,ohm.$$ This resistance of the wire will be $$2\,ohm$$ at.
The electrostatic field due to a point charge depends on the distance $$r$$ as $$\frac{1}{{{r^2}}}.$$ Indicate which of the following quantities shows same dependence on $$r.$$
A.
Intensity of light from a point source.
B.
Electrostatic potential due to a point charge.
C.
Electrostatic potential at a distance r from the centre of a charged metallic sphere. Given $$r$$ < radius of the sphere.