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

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:

$\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}$  (1)

Where: $R_{1}=2k\Omega$, $R_{2}=6k\Omega$, $R_{3}=10k\Omega$

Solving (1):

$\frac{1}{R}=\frac{1}{2k\Omega}+\frac{1}{6k\Omega}+\frac{1}{10k\Omega}$  (2)

$\frac{1}{R}=\frac{23}{30k\Omega}$  (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:

$P=\frac{V^{2}}{R}$   (5)

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

Solving:

$P=\frac{(100V)^{2}}{1304.34\Omega}$   (6)

Finally:

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