Answer to Question #155916 in Electric Circuits for Jerick

Question

Six Christmas tree lights are arranged in parallel circuit as shown in the figure. Each bulb dissipates 10W when operated at 120V. (a) What is the resistance R of each bulb? (b) What is the resistance of the entire array of bulbs? (c) What is the total power consumption of the array? (d) What are the currents at points a, b, c, and d?

Answer 1

The current through each bulb:

$I_b=I_c=I_d=\frac{P_{bulb}}{U}=\frac{10}{120}=83.3\space mA,$

where $P_{bulb}$ -  power, dissipated on each bulb;

U - voltage across parallel circuit.

The current at point a:

$I_a=I_b+I_c+I_d=250\space mA.$

The resistance of the entire array of bulbs:

$R=\frac{U}{I_a}=\frac{120}{0.25}=480\space Ohm.$

The resistance of each bulb:

$R_1=R_2=R_3=\frac{U}{I_b}=\frac{120}{0.0833}=1.44\space kOhm.$

The total power consumption of the array:

$P=UI_a=120\cdot0.25=30\space W.$

Answer:

(a) 1.44 kOhm

(b) 480 Ohm

(c) 30 W

(d) $I_a=250\space mA.$

$I_b=I_c=I_d=83.3\space mA.$