Basics of Network Theory (Solved Problem 7) | Problem on Bulbs

Network Theory: Basics of Network Theory (Solved Problem 7) | Problem on Bulbs
Topics discussed:
1) Meaning of incandescent bulb.
2) Series combination of bulbs.
3) Parallel combination of bulbs.
4) Total power when the bulbs are connected in series.
5) Solution of GATE-2001 (EE) network theory problem on series arrangement of bulbs.
6) GATE-2009 (EE) network theory problem on the series combination of bulbs as the homework problem.

Music:
Axol x Alex Skrindo - You [NCS Release]

#NetworkTheoryByNeso

[zahidhasankhoka]

Option d.
From 100W/220 V we can calculate R=V^2/P and the value is 484 ohm.
Similarly, from 200W/220 V we can calculate R value according to the formula P= v^2/R. Then we can find R is 242 ohm.
Therefore, number of bulb in series is 484/242 =2.

[adi-egoistic]

First, let's find the resistance of the 100W lamp:
P = V^2 / R
100 = 220^2 / R
R = 220^2 / 100
R = 484 ohms Now, for the 200W lamps:
P = V^2 / R
200 = 220^2 / R
R = 220^2 / 200
R = 242 ohms Since the lamps are connected in series, the total resistance is the sum of the individual resistances. Let's denote the number of 200W lamps as n. Total resistance for the 200W lamps = n * 242 We want this total resistance to be equal to 484 ohms, the resistance of the 100W lamp:
n * 242 = 484
n = 2

[abhishekshukla]

Sir if we consider P= I^2R then Power will be directly proportional to the resistance. Then how did we conclude that power is inversely proportional to the resistance just from P= V^2/R.

[Brett]

Sir also add some topics on Power System Analysis and Control System

[dhyangandhi]

Sir, Vm^2/R1 should not equal to P1.
We initially said that P1= i^2R1.
If the first equation I have written is correct as well, then it will amount to Vm= iR1..which is not true.
Vm=i(R1+R2)

[pankajdheer]

Incandescent lamps capacity = 200W

Lamp current = 200W/220V = 0.91A

Lamp resistance = 220V/0.91A = 242 ohms.

If two lamps are connected in series the resistance = 242 x 2 = 484 ohms

The voltage across individual lamp = 220V/2 = 110V

The current through a lamp = 110V/242 ohms = 0.45A

Power consumed by each lamp = 0.45x0.45x242ohms = 49W

The total power of 2 lamps connected in series = 49W+49W=98W

Approximately 2 lamps in series circuit consume 98W under 22

[vijayapriyas]

To find total power, you replaced Vm^2/r1 by Pr1, how is it comes? please explain...

[Manicrover]

Dubt:
U concluded P_r ∝ 1/r, from P_r=V²/r
But, if we consider P_r=I²r, we can conclude p_r ∝ r
Which is contradictory with first conclusion.
How do I know that it is the first conclusion that we have to consider?

[avethakur]

At 3:39 ....do you mean that V(rated) is constant for both bulbs?

[truptichaudhary]

Is this right?
Total power of lamp is Sam for both parallel n series i.e r1r2/r1+r2