In all three figures above, the resistors represent light bulbs each with resist

Question

In all three figures above, the resistors represent light bulbs each with resistance of 20 Ohm. What is the equivalent resistance of (A) above? What is the equivalent resistance of (B) above? If the resistors in (B) are connected to a 9V source, what is the current through the two resistors in parallel? The amount of light produced by a light-bulb will increase with increasing current. A 24 V battery is attached to the two ends of arrangement (C) making a complete circuit. Rank the resistors by increasing light output. Find the power used in R4 (arrangement C tied to a 24V battery).

Explanation / Answer

(1)
Equivalent resistance of A, = 1/(1/20 + 1/20) = 10

(2)
Equivalent resistance of B, = 20 + 1/(1/20 + 1/20) = 20 + 10 = 30

(3)
V = I* R
I = 9/30
I = 0.3 A,
Current through resistors in paralle, = 0.3/2 = 0.15 A

(4)
R1 > R2 > R3 = R4

(5)
Req = 20 + 1/(1/20 + 1(20+20)) = 33.33
I = 24/33.33 = 0.72 A

Current through R4, = (24 - 0.72*20) / (40) = 0.24 A

Power used in R4, = 0.24^2 * 20 = 1.15 W

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