Electronics - Parallel Circuits - Discussion

Total power reading of the wattmeter is 9.408.

If you solve for the individual powers in the branches:

P = V^2/R.
P1 = 2.304W , P2 = 1.152W , P3 = 0.768W &, P4 = 0.576W.

If you get the total power:
P1+P2+P3+P4 = 4.8 W which is smaller than the reading in the ammeter which definitely tells us that something is wrong with the circuit.

Now since there are ammeters connected in between the branches we can check if the individual values of branch currents match the readings.

First in R2, I2 = 48/2000 = 24mA.
In R3, I3 = 48/3000 = 16mA.
In R4, I4 = 48/4000 = 12mA.

From the Ammeter Connected in-branch R4 we can confirm that it is correct since it has the same reading of 0.012 or 12mA.

From the Ammeter Connection in-branch R2 the reading is 0.052 A or 52mA since we know that I2 = 24mA, via Kirchoff's Current Law 52mA=24mA+ I , I is the current that would go to the branch R3. I = 28mA.

Since we know that I3 = 16mA, Via Kirchoffs Current Law we can check that, I = I3 + I4; 28mA =16mA+12mA.

Since we confirmed that I3 and I4 is correct it also implies that the current in I2 is correct therefore all of the power ratings of P2, P3, and P4 is correct thus indicating that R1 is of the wrong value.

Given total power=9.408
Power of r1=48/1*1000=.48mW
r2=48/2*1000=.24mW
r3=48/3*1000=.16mW
r4=48/4*1000=.12mW

Total power = 1W
But the total power given=9.408W.
ie, one resistor is wrong value.
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0.012A is current through R4
I R4= 48/4*1000 = .012A

So R4 is correct value
.................................................................

0.053 is the current total through r2, r3 and r4 as branch current total.
.........................................................................

We know that current through R4=.012

I (R2+R3) = V/(R2*R3/R2+R3)

=48/(2*3/2+3)1000
=48/(6/5)1000
=48/1200
=.04

Then I(R2+R3+R4)= .04+.012 = .052

So that R2,R3,R4 are correct.

i.e. R1 is wrong

P = VxIt
It = P/V = 9.408/48 = 0.196A (Total Current)

IR4 = 0.012 A (Given)

R4 = 48/0.012 = 4000 = 4K R4 is correct

IR3 = V/R3 = 48/3000 = 0.016A
IR2 = V/R2 = 48/2000 = 0.024A
IR1 = V/R1 = 48/1000 = 0.048A

IR3 = (I3-I4)
I3 = (IR3+I4)
I3 = (0.016+0.012)=0.028A

R3 = V/(I3-I4) = 48/(0.028-0.012) = 3000 = 3K R3 is correct

R2 = V/(I2-I3) = 48/(0.052-0.028) = 2000 = 2K R2 is also correct

R1 = V/(It-I2) = 48/(0.196-0.052) = 333.33ohms which is notcorrect

since R1=1000ohms = 1k from the given circuit

Total current in circuit is I= p/v; 9.408/48 = 0.196.

And sum of current through r2, r3 & r3 equals to 0.052.

Current through r1 is 0.048.

And sum of the current through r1, r2, r3, and r4 is 0.102.

The difference between this is 0.196 - 0.102 = 0.092.

They r1 has wrong value r1 t = should have value 144K ohm.

Guys suppose if R1 is ok 333 ohm but problem is with R2 or R3. Then how it will be opted out which one (R2 or R3) is not correct because before R2 we have a given value 0.052 and after R3 also given 0.012 but is not given between R2 & R3.

Please explain although might not look a problem to you.

One way to start is that, the power comes from the smallest resistor. So, after verifying that currents through R3 and R2(0.04A) and R4(0.012) sum up to 0.052A, we search for a smaller value for R1 that could elevate the power to 9.408W which is exactly 1/3K.

I1=V/R=48/1K=48mA=0.048A
It=I1+0.052(in circuit itself)
It=0.048+0.052=0.1A
It=0.1A

P=VI
P=48*0.1=4.8W

so the watt meter reading should be 4.8 watts but the circuit shows 9.408W.

so mistake in R1.

Answer is A

P = V*I .... I = P/V = 9.408/48 = 0.196A (Total Current)
Current on R1 = 0.196 - 0.052 = 0.144A
R1 = 48V/0.144A = 333.33 Ohm (Should be the correct value of R1)

@H@Ri.

Your explanation is good but please tell me power = V^/R or v/r in your explanation you describe that p=v/r. Please explain anyone.

I=v/r so I=48/1*10^3
so i=0.48
but here ammeter shows the value of 0.053
so here we have to change the value of resistance.