When voltage changes its direction after every half cycle is known as alternating voltage. The current flows in the circuit at that time are known as alternating current. The alternating current(AC) follows the sine function which changes its polarity concerning time. Most of the electrical devices are operating on the ac voltage.
Acids and Bases
$P = - \frac{xx^T}{x^Tx}$Acid is any hydrogen-containing substance that is capable of donating a proton (hydrogen ion) to another substance. Base is an ion or molecule capable of accepting a hydrogen ion from acid.
Physical Properties of Acids and Bases
Physical Properties
ACIDS
BASES
Taste
Sour
Bitter
Colour on Litmus paper
Turns blue litmus red
Turns red litmus blue
Ions produced on dissociation
H+
OH-
pH
<7 (less than 7)
>7 (more than 7)
Strong acids
HCl, HNO3, H2SO4
NaOH, KOH
Weak Acids
CH3COOH, H3PO4, H2CO3
NH4OH
Chemical Properties of Acids and Bases
Type of Reaction
Acid
Bases
Reaction with Metals
Acid + Metal → Salt + Hydrogen gas (H2)
E.g.,
Zn(s)+ dil. H2SO4 → ZnSO4 (Zinc Sulphate) + H2
Base + Metal → Salt + Hydrogen gas (H2)
E.g.,
2NaOH +Zn → Na2ZnO2 (Sodium zincate) + H2
Reaction with hydrogen carbonates (bicarbonate) and carbonates
Metal carbonate/Metal hydrogen carbonate + Acid → Salt + Carbon dioxide + Water
$P = - \frac{xx^T}{x^Tx}$The a3 + b3 formula can be verified, by multiplying (a + b) (a2 - ab + b2) and see whether you get a3 + b3. The a3 + b3 formula or the difference of cubes formula is explained below:
a3 + b3 Formula = a3 + b3 = (a + b) (a2 - ab + b2)
You can remember these signs using the following trick.
Let us learn the a3 + b3 formula with a few solved examples.
Proof of a^3+ b^3 Formula
Let us see the verification of a cube plus b cube formula here. To prove or verify that a3 + b3 = (a + b) (a2 - ab + b2) we need to prove here LHS = RHS. Lets begin with the following steps. LHS = a3 + b3 On Solving RHS side we get, = (a + b) (a2 - ab + b2) On multiplying the a and b separately with (a2 - ab + b2) we get = a (a2 - ab + b2) + b(a2 - ab + b2) = a3 - a2b + ab2 + a2b - ab2 + b3 = a3 - a2b + a2b + ab2- ab2 + b3 = a3 - 0 + 0 + b3 = a3 + b3 Hence proved, LHS = RHS
