Question

A circuit contains three resistors connected in parallel. The value of R1 is 2 K , the value or R2 is 6 K , and the value of R3 is 10 K . If the supplied voltage is 100 VDC, what is the total power in the circuit?

A. 2.18 W

B. 8.18 W

C. 7.67 W

D. 4.24 W

(Can someone help me understand how to get the answer?)

Answer 1

Answer: C. 7.67 W

Step-by-step explanation:

Firstly, we are told the three resistors are connected in parallel, this means we have to use the following equation to find the total resistance
`R` of the circuit:

`(1)/(R)=(1)/(R_(1))+(1)/(R_(2))+(1)/(R_(3))` (1)

Where:
`R_(1)=2k\Omega`,
`R_(2)=6k\Omega`,
`R_(3)=10k\Omega`

Solving (1):

`(1)/(R)=(1)/(2k\Omega)+(1)/(6k\Omega)+(1)/(10k\Omega)` (2)

`(1)/(R)=(23)/(30k\Omega)` (3)

`R=1.3043k\Omega}=1304.34\Omega` (4) This is the total resistance of the circuit

On the other hand, the total power
`P` of this circuit is given by the following equation:

`P=(V^(2))/(R)` (5)

Where
`V=100V` is the total voltage of the circuit.

Solving:

`P=((100V)^(2))/(1304.34\Omega)` (6)

Finally:

`P=7.67V\Omega=7.67W` (7) This is the total power of the circuit in Watts (W)