Electrical Engineering - Series-Parallel Circuits - Discussion

470ohm and 1500ohm are in parallel hence effective resitance is=470*1500/1970
=357.87ohm

Parallel combination of 5 1kohm resistors=1000/5=200ohm

Now toatal effective resistance=357.87+200=557.87ohm

Hence current in the circuit=50/557.87=.089amp

Now current throuh 5 1kohm resistors can be divided into two parallelcombination one with resistance 1kohm and other with 1/4kohm...........

Hence by current divider rule current through 1kohm resistor=(.089*1/4)/(1+1/4)=.018amp

Hence % = (.018/.089)*100 = 20%.

From Priya calculations, we get:

Current in circuit = .089 A.

Total resistance in parallel combination of 5 1 Kohm resistors = 200 Ohm.

So, voltage in parallel of 5 1kohm resistor = I x R(total res of paralleled 5 resistors).

= .089 x 200.

= 17.8 V.

For parallel combinations, V = V1 = V2 = V3 = V4.

So. V1 = I1 R1.

I1 = V1/R1 = 17.8/(1x10^3) = 0.0178 A.

For percentage, I1/whole circuit current x 100% = 0.0178/.089 x 100.

= 0.2 x 100.

= 20%.

I am 100% agree with the solution given by Meena, it is the simplest & quick way of calculation. The total current flowing out from the first parallel combination will flow in the second combination but will get divided in to five equal parts so each part of current will be i/5th of the combination(2nd) total input current which will be 1/5th i.e..2 or.2*100 = 20%.

Of course @Meena you are right.

But this simple and quick method is only applied when all the resistors are of same value. Otherwise you can't applied when resistors are of different values are given.

What is the simple method when resistors are of different values are given?

Current I flowing in the circuit will be divided into 5 equal parts (as the 5 equal valued resistors are connected in parallel).

So the current in each branch (of resistor) is I/5.

So the percentage is : (I/5) /I*100 = 20%.

The simplest way is to decide the correct ans. is the total current is passed through five parallel 1k resister equal amount bcoz the same value of resister so 1k current flow=total current (%)/number of resister; 20%.

@Meena.

You are wrong in parallel current through all branches is not same :).

You are getting the right answer because all resistors are same value so the currents drawn by them is also same :).

Actually, they ask for a percentage. So, for 51K ohms resistor 50V/200ohm = 0.25A.
Again 50/1 Kohm = 0.05A, therefore 0.05/0.25*100 = 20%.

@Meena.

Exactly your right for same set of resistors. And even we can calculate the same in for different resistors values.

Five 1k ohm parrallel R=200..
i =V/R =50/200=0.25.
i for 1k, i = 50/1000 = 1/20 = 0.05.
i %=0.05 * 100/0.25 = 20%.