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 [tex]R[/tex] of the circuit:
[tex]\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}[/tex] (1)
Where: [tex]R_{1}=2k\Omega[/tex], [tex]R_{2}=6k\Omega[/tex], [tex]R_{3}=10k\Omega[/tex]
Solving (1):
[tex]\frac{1}{R}=\frac{1}{2k\Omega}+\frac{1}{6k\Omega}+\frac{1}{10k\Omega}[/tex] (2)
[tex]\frac{1}{R}=\frac{23}{30k\Omega}[/tex] (3)
[tex]R=1.3043k\Omega}=1304.34\Omega[/tex] (4) This is the total resistance of the circuit
On the other hand, the total power [tex]P[/tex] of this circuit is given by the following equation:
[tex]P=\frac{V^{2}}{R}[/tex] (5)
Where [tex]V=100V[/tex] is the total voltage of the circuit.
Solving:
[tex]P=\frac{(100V)^{2}}{1304.34\Omega}[/tex] (6)
Finally:
[tex]P=7.67V\Omega=7.67W[/tex] (7) This is the total power of the circuit in Watts (W)
