Given
V=9
R1=10k ohm
R2=2k ohm
R3=1k ohm
And find v1,v2,It,Rt,PT in parallel circuit with explanation
To find v1 and v2 in a parallel circuit, we can use the following formulas:
v1 = V * (R2 || R3) / (R1 + R2 || R3)
v2 = V * R1 / (R1 + R2 || R3)
where "||" represents the parallel combination of resistors.
First, let's calculate the parallel combination of R2 and R3:
R2 || R3 = (R2 * R3) / (R2 + R3)
= (2000 * 1000) / (2000 + 1000)
= 2000000 / 3000
= 666.67 ohm (approx.)
Now we can substitute this value into the formulas to find v1 and v2:
v1 = 9 * (666.67) / (10000 + 666.67)
= 5999.96 / 10666.67
= 0.5625 volts (approx.)
v2 = 9 * 10000 / (10000 + 666.67)
= 90000 / 10666.67
= 8.44 volts (approx.)
Next, let's calculate It (total current) and Rt (total resistance) in the parallel circuit:
It = V / Rt
Rt = (R1 || R2 || R3)
To calculate Rt, we need to calculate the series combination of R1, R2, and R3:
R1 || R2 || R3 = (1 / (1/R1 + 1/R2 + 1/R3))
= (1 / (1/10000 + 1/2000 + 1/1000))
= (1 / (0.0001 + 0.0005 + 0.001))
= (1 / 0.0016)
= 625 ohm (approx.)
Now we can substitute this value into the formulas to find It:
It = 9 / 625
= 0.0144 A (approx.)
Finally, let's calculate PT (total power) in the parallel circuit:
PT = It * V
= 0.0144 * 9
= 0.1296 W (approx.)
So, in summary:
v1 = 0.5625 volts
v2 = 8.44 volts
It = 0.0144 A
Rt = 625 ohm
PT = 0.1296 W