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^Galvanometer

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

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.

^Instantaneous velocity

^Instantaneous velocity

Velocity a particular instant is called instantaneous.

At any point instantaneous velocity acts along the tangent at that point. Mathematically it is measured as the limiting value of the average velocity.

For motion along x – axis,   

Initial means, starting time i.e. t = 0

  1. For 1 D motion along x – axis we have,  i.e. instantaneous velocity is equal to slope of position time graph (x – t).

2. On separating the variables & integrating this relation can be rearranged as

i.e. area under x – t graph bounded with the time axis for a time interval is equal to displacement for that time interval.

^n – cells in series

n – cells in series

As all the cell supply current in same direction thus

^Error in exponential form

^Error in exponential form

Differentiating both sides we can write

The maximum value of fractional error will be

^+ ve α for metals & alloys

+ 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

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.

^Series grouping of capacitors

Series grouping of capacitors

1. Charge on all the components connected in series is same (i.e. q = constant).

2. Potential difference is divided among the various capacitors in accordance with  e. a capacitor of smaller capacitance will get more potential difference & vice versa.

3. Effective capacitance is given by,

^PPC with a metal slab in plates

PPC with a metal slab in plates

If a metal slab (dielectric constant K = ∞), thickness t < d is placed between the plates of a PPC, then due to the electric field between the capacitor plates the dielectric gets polarized & an electric equal to E0 is induced in it, as a consequence net electric field in dielectric is found to be zero i.e. Enet = 0.

Due to this field electric field net potential difference across the capacitor plates becomes

Using C = q/V, capacitance of capacitor becomes

If the conducting slab occupies the entire space available between the plates of capacitor i.e. when t =d & K = ∞, then C = ∞

Comparing (a), (b) & (c) we can say

CDS > CCS > Co

*What is a scalar?

*What is a scalar?

If a physical quantity can be completely described by telling its magnitude only and direction is meaningless for it, then it is called a scalar.

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