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. (1) What is the equivalent resistance of (A) above ? What is the equivalent resistance of (B) above? (3) 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 24V battery is attached to the two ends of arrangement (c) making a complete circuit Rank the resistors by increasing light output.

Explanation / Answer

a) the resistances are in parallel, so the equivalent resistance = 1/(1/R + 1/R) = R/2 = 20/2 =10ohm

b) It is same case in which there is additional resitance (R) in series with the case as in part a)

so, the net resistance = R in series with R/2 = R+R/2 = 3R/2 = 3*20/2 = 30 ohm

c) The net current in the circuit = Total voltage/ net resistance = 9V/(30 ohm) = 0.3 A

so, the current through the parallel resistance will be half of the net current = 0.3A/2 = 0.15 A

d) R1 will be highest, R2 will be second highest and lastly R3=R4

e) Now, r3 and r4 are in series so the net resistance between them = r3 + r4 = 40 ohm

now it is in parallel with r2 so, the net resistance = 1/(1/20 + 1/40) = 13.33 ohm

now this is in series with r1 so the net resistance = r1+13.33 = 20 + 13.33 = 33.33 ohm

so, the power will be = voltage^2/net resistance = 24^2/33.33 = 17.28 W

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