@ three resistors r1,r2,r3 are connected in 1)parallel and 2) series . Write the expression of equivalent resistance in each case..
B two identical resistances of 12 ohms each are connected to a battery of 3v. Caluclate the ratio of power consumed with maximum resistance and minimum resistance.
I did everything correct but I think so I am not sure whether I wrote ratio or not.. please anyone tell how many marks are deducted for ratio....
Answers
Q. Problem 1 -
# Answer -
When r1, r2 & r3 are connected in parallel, equivalent resistance is -
Rp = (r1r2 + r2r3 + r1r3) / (r1r2r3)
When r1, r2 & r3 are connected in series, equivalent resistance is -
Rs = r1 + r2 + r3
Q. Problem 2 -
# Answer -
Maximum resistance is provided by series combination -
Rs = 12 + 12 = 24 ohm
Minimum resistance is provided by parallel combination -
Rp = 12 / (1+1) = 6 ohm
Ratio of power consumed -
Ps/Pp = Rp/Rs
Ps/Pp = 6/24
Ps/Pp = 1/4
Ratio of power consumed by max vs min resistance is 1:4.
Hope this helped you...
@ three resistors r1,r2,r3 are connected in 1)parallel and 2) series . Write the expression of equivalent resistance in each case..
B two identical resistances of 12 ohms each are connected to a battery of 3v. Caluclate the ratio of power consumed with maximum resistance and minimum resistance.
I did everything correct but I think so I am not sure whether I wrote ratio or not.. please anyone tell how many marks are deducted for ratio....
Resistance in Series
Rtotal = R1 + R2 + R3
Resistance in Prallell
1/RTotal = 1/R1 + 1/R2 + 1/R3
1/RTotal = (R2R3 + R1R3 + R1R2)/R1R2R3
RTotal = R1R2R3/(R2R3 + R1R3 + R1R2)
if identical resistance connected in series
12 Ω with 3V
Total Resistance = 12 + 12 = 24 Ω
Power total = V²/Rtotal = 3²/24 = 9/24 = 3/8 W
Current is same in series
I = V/Rtotal = 3/24 = 1/8
Power consumed in 1 resistance = I²R = (1/8)² * 12 = 12/64 = 3/16 W
Ratio = (3/16)/(3/8) = 1/2
if identical resistance connected in Parallel
12 Ω with 3V
Total Resistance = (12*12)/(12 + 12) = 6 Ω
Power total = V²/Rtotal = 3²/6 = 9/6 = 3/2 W
Voltage is same in parallel
Power consumed in 1 resistance = V²/R = 3² /12 = 9/12 = 3/4 W
Ratio = (3/4)/(3/2) = 1/2
Ratio of power in parallel / Series = (3/2) / (3/8) = 4 : 1