Advertisements
Advertisements
प्रश्न
1 MW power is to be delivered from a power station to a town 10 km away. One uses a pair of Cu wires of radius 0.5 cm for this purpose. Calculate the fraction of ohmic losses to power transmitted if
- power is transmitted at 220 V. Comment on the feasibility of doing this.
- a step-up transformer is used to boost the voltage to 11000 V, power transmitted, then a step-down transfomer is used to bring voltage to 220 V. (ρCu = 1.7 × 10–8 SI unit)
Advertisements
उत्तर
i. When power is transmitted at 220 V.
Power lost in transmission P = I2R
| P = VI |
P = 1 MV = 106 W
V = 220 Volt
`I = P/V = 1000000/220`
`I = 50000/11 A`
| R = `ρ I/A` |
⇒ R = `(ρl)/(pir^2)`
I = 10 km × 2 = 20,000 M
∴ A = πr2
r = 0.5 cm = 0.5 cm × 10–2 = 5 × 10–3 cm
ρCu = 1.7 × 10–8 Ωm
R = `(ρI)/A`
∴ R = `(1.7 xx 10^-8 xx 20,000)/(3.14 xx 5 xx 10^-3 xx 5 xx 10^-3)`
= `(170 xx 20000 xx 10^(-8+6))/(314 xx 5 xx 5)`
= `(170 xx 20000)/(314 xx 25 xx 100)` Ω
R = `(170 xx 800)/(314 xx 100) = (170 xx 4)/157 = 680/157` ≅ 4Ω
∴ Power loss = I2R
= `50000/11 xx 50000/11 xx 4 = (100 xx 10^8)/121 = 8.26 xx 10^7`
Power loss in heating = 82.6 MW
As 82.6 MW > 1 MW
So this method cannot be used to transmit the power.
ii. When power is transmitted at 11000 V
P = 106 W
VI = 1000000
11000 I = 1000000
`I = 1000000/11000 = 1000/11`
∴ RCu = 4Ω as already calculated in part (i)
∴ Power loss = P = I2R
P = `1000/11 xx 1000/11 xx 4 = 4000/121 xx 4^4`
P = `3.3 xx 10^4` Watt
Fractional power loss = `(3.3 xx 10^4)/10^6 = 3.3/1000` = 0.033
Power loss in 3.3%
APPEARS IN
संबंधित प्रश्न
State the principle of transformer working with the help of a diagram
The teachers of Geeta’s school took the students on a study trip to a power generating station, located nearly 200 km away from the city. The teacher explained that electrical energy is transmitted over such a long distance to their city, in the form of alternating current (ac) raised to a high voltage. At the receiving end in the city, the voltage is reduced to operate the devices. As a result, the power loss is reduced. Geeta listened to the teacher and asked questions about how the ac is converted to a higher or lower voltage.
1) Name the device used to change the alternating voltage to a higher or lower value. State one cause for power dissipation in this device.
2) Explain with an example, how power loss is reduced if the energy is transmitted over long distances as an alternating current rather than a direct current.
3) Write two values each shown by the teachers and Geeta.
Explain the significance of Lenz’s law to show the conservation of energy in electromagnetic induction.
The transformer is used in ______ current circuits.
State the principle of working of a transformer. Can a transformer be used to step up or step down a d.c. voltage? Justify your answer.
Why is the core of a transformer made of soft iron?
A transformer lowers e.m.f. from 220 V to 15 V. If the number of turns in primary are 3520, how many turns are in the secondary coil?
Transformer works on ______.
Explain the construction of transformer.
Give the advantage of AC in long distance power transmission with an illustration.
A 200V/120V step-down transformer of 90% efficiency is connected to an induction stove of resistance 40 Ω. Find the current drawn by the primary of the transformer.
Read the following paragraph and answer the question:
Long distance power transmissions
The large-scale transmission and distribution of electrical energy over long distances is done with the use of transformers. The voltage output of the generator is stepped up. It is then transmitted over long distances to an area sub-station near the consumers. There the voltage is stepped down. It is further stepped down at distributing sub-stations and utility poles before a power supply of 240 V reaches our homes.
We need to step-up the voltage for power transmission, so that ______.
For an LCR circuit, the power transferred from the driving source to the driven oscillator is P = I2Z cos φ.
- Here, the power factor cos φ ≥ 0, P ≥ 0.
- The driving force can give no energy to the oscillator (P = 0) in some cases.
- The driving force cannot syphon out (P < 0) the energy out of oscillator.
- The driving force can take away energy out of the oscillator.
The primary coil having NP turns of an ideal transformer is supplied with an alternating voltage VP. Obtain an expression for the voltage VS induced in its secondary coil having NS turns.
Mention two main sources of power loss in real transformers.
What does the laminated soft iron core provide for the flux?
Which winding is the input coil connected to the AC source?
Which law relates the changing flux to the EMF induced in both coils?
