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*Describing a vector

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*Describing a vector

A vector can be expressed as infinite no. of components in 2D or 3 D, however generally a vector is expressed as the resolution of three mutually perpendicular components

a, b & c along x, y & z axis respectively.

Here (a, b, c) are also called direction ratios of  .

Length of a vector is called its magnitude .. Magnitude of is described as, 

Let makes angle θx, θy & θz with the x, y & z axis respectively. cos of these angels are called direction ratios of  & usually expressed in terms of symbols (l, m, n) & are related to direction ratios as

Magnitude of a unit vector is unity i.e.

*Kinematics

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*Kinematics

^Electrolysis

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Electrolysis

  • The process of dissociating a liquid into ions when electric current is passed through them is called electrolysis or conductors of second kind. The arrangement used to study electrolysis is called a Voltameter. It contains a vessel, two electrodes, a solution called electrolyte & dc power supply.
  • Current inside electrolytes is due to motion of both + ve & – ve ions. i.e. I = I+ + I–  also I+ ≠ I–. 
  • Electrolysis obey Ohm’s law for small currents if V applied > V back.
  • Conductivity of electrolytes is 105  to 106 times smaller than that of metallic conductors.

^Wheatstone bridge

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Wheatstone bridge

It is the quadrilateral arrangement of four resistors P, Q, R & S connected to a cell & galvanometer G as shown. Here P & Q are called ratio arms, R known arm & S unknown arm.

1. If , then VC = VD & the bridge is said to be balanced i.e. the potential difference across the arm CD is zero, consequently no the current through the arm CD & thus arm CD can be removed. Also the position of cell & galvanometer can be interchanged.

2. If , then VC ≠ VD & bridge is said to be in the unbalanced state. If  then current flows from up & if  then current flows down.

3. Wheatstone bridge is said to be sensitive if all the four resistances are of the same order i.e. when the current in the four branches is of the same order. In this case error associated with the measurement of X is mini.

^Galvanometer

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Galvanometer

A current carrying coil placed in a magnetic field experiences a torque & deflects.

This deflection is calibrated to measure current flowing in it. Used to detect & measure only small currents of the order of microamperes. Current sensitivity (Is): It is defined as the deflection produced for a unit current. i.e. . Is can be increased by increasing B or by decreasing k (by taking quartz or phosphorous bronze). Reciprocal of current sensitivity is called ‘figure of merit’. As we have discussed that a galvanometer fails to measure currents I > Ig. In order to measure currents I > Ig we use an Ammeter.

^CR circuits

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With switch S thrown towards A, capacitor undergoes charging in accordance with

With switch S thrown towards B, capacitor undergoes discharging in accordance with

Here CR = t is called capacitive time constant.

Following table is useful to solve problems based on exponential functions.

^n – cells in series

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n – cells in series

As all the cell supply current in same direction thus

^Significant figures

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^Significant figures

All accurately known digits plus the first uncertain digit of a measurement is called significant digits or significant figures. e.g. if in a measurement, mass of a body lies between 5.6 kg & 5.7 kg & we estimate it as 5.62 kg then the first two digits 5 & 6 are certain while the third digit 2 is approximately known we can say there are 3 significant figures.

Following are the rules for counting significant figures

Rule 1: All non zero digits are significant.

Rule 2: All zeros occuring between two non zero digits are significant.

Rule 3: The digit zero (underlined) conventionally put on the left of a decimal for a number less than one is never significant. All zeros to the right the decimal point are not significant.

Rule 4: The terminal or trailing zero(s) in a number without a decimal point are not significant.

Rule 5: The trailing zero(s) in a number with a decimal point are significant.

Rule 6: The powers of ten are not significant.

Rule 7: No. of significant figures remains unchanged on changing the units of measurement, zeroes appearing in the base number in the scientific notation are significant.

Example NSD Using rule
4567 Four 1
450067 Six 2
0.004567 Four 3
456700 Four 4
0.00456700 Six 5
4.5 x 10 – 6 Two 6
5.300 x 10 6 mm Four 7

^+ ve α for metals & alloys

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+ ve α for metals & alloys

With the increase in temperature of metals & alloys thermal agitation increases & hence the rate of collision increases. As a result the average time t between the successive collision decreases & hence the drift speed decreases, consequently the resistivity of metals increases.

^Ohm’s law

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Ohm’s law

(a) = constant called electrical resistance R, provided there is no change in the physical conditions like temperature, pressure & impurity etc.

(b) = (Microscopic version) i.e. conductivity of a conductor is independent of electric field existing in the material over a wide range of field.

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