Current Electricity Concept Page - 14

Definition

Power transmission

• Generating station: Electrical power is generated at 11 kV and 50 Hz.
• Step-up transformer: Voltage is stepped up to 33 kV reducing current to 1/3rd and hence reducing heat losses in the wire.
• Transmission: Transmission is done at 33 kV.
• Step-down transformer: Voltage is stepped down to 220 V for consumer use.

Definition

Describe a watt hour meter

Electricity reaching our house through electric lines enter the watt hour meter first. then it passes through the main switch to different appliances. the commercial unit of consumption of consumption of electrical energy is kWh$kWh$. The watt hour meter is the instrument which is used for measuring the energy consumed in kilowatt hour (kWh$kWh$).

Example

Domestic electrical circuits

The major components of domestic electrical circuits are:

• Supply lines: Live wire (red), earth wire (green) and neutral wire (black). Potential difference between live wire and neutral wire is 220 V.
• Earth wire is connected to a metal plate deep inside the ground for safety purpose.
• Live wire and neutral wire enter electricity meter via a main fuse (used for protection).
• Two separate circuits of different current ratings (5A and 15 A) are used.
• All components are used in parallel and hence are supplied by same potential difference of 220 V. Currents in the loads vary according to requirement. Also, this allows to separately handle each load. It also reduces the overall resistance of the load.
• Fuses are used in the circuit for protection in the circuit against huge current values due to short circuit and overloading.

Definition

Local earthing

Local earthing is made near the kWh meter in a house. A copper rod is connected to a copper plate which is buried inside the ground. Whenever the current in the circuit exceeds a value, it is sent to the ground with the help of the earthing wire.

Example

Earthing an appliance

It is essential to provide an earthing connection to an electrical appliance. When a faulty wire comes in contact with the metal body of the appliance, it acquires a high potential and can cause severe shocks. These are prevented by earthing the appliance which drives the potential to zero.

Definition

Relationship between current and voltage of a capacitor

The relationship between a capacitors voltage and current define its capacitance and its power. We have Q=CV.
Then $$\dfrac{dQ}{dt}=C \dfrac{dV}{dt} \Rightarrow i_c=C \dfrac{dV_c}{dt}$$

Definition

Voltage across a capacitor doesn't change suddenly

i=CdVdt$i=C{\displaystyle \frac{dV}{dt}}$
An instantaneous change in the voltage across a capacitor would require taking limits.
limt→0i=Climt→0dVdt$\underset{t\to 0}{lim}i=C\underset{t\to 0}{lim}\frac{dV}{dt}$
i.e. the rate of change of the voltage (dv/dt) be infinite, and hence the current would have to be infinite which is not possible.

Definition

Behaviour of capacitor on closing the switch

Voltage across a capacitor does not change suddenly. Hence, for an uncharged capacitor, just after the switch is closed voltage remains zero. This is analogous to a short circuit. Hence, an initially uncharged capacitor behaves as a short circuit just after closing the switch. 
Example:
Find the current in the circuit shown in the attached figure just after the closing of the switch. The capacitor is initially uncharged.
Solution:
Just after the closing of the switch, capacitor behaves as a short circuit. Hence, the current is given by:
I=VsR$I={\displaystyle \frac{V_s}{R}}$

Example

Capacitor as an open circuit

In the steady state, the energy stored in the capacitor is :In steady state current flow in capacitor branch is zero.

I=E1R1+R2+r1$I={\displaystyle \frac{E_1}{R_1+R_2+r_1}}$
⇒VC−E2=IR1$\Rightarrow V_C-E_2=I{R}_1$

VC=E2+R1E1R1+R2+r1$V_C=E_2+{\displaystyle \frac{R_1{E}_1}{R_1+R_2+r_1}}$
Energy stored =12cv22$={\displaystyle \frac{1}{2}}c{v}_2^2$
                         =12c[E2+R1E1R1+R2+r1]2$={\displaystyle \frac{1}{2}}c[E_2+{\displaystyle \frac{R_1{E}_1}{R_1+R_2+r_1}}{]}^2$

Example

RC circuits at the time of closing of switch

Only switch S1$S_1$ closed in Figure. What is the charge on the 3μF$3\mu F$ capacitor in μC$\mu C$?Without power supply V=12$V=12$ we can not solve.
When S1$S_1$ is closed only , the capacitance 3μF$3\mu F$ is charged to voltage V=12$V=12$.
Thus, the charge on 3μF$3\mu F$ is Q=3V=3×12=36μC

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