Answer the following questions based on the circuit in Fig. 8. When switches Si

Question

Answer the following questions based on the circuit in Fig. 8. When switches Si and Si are open, the ammeter reading is 0.6 A and voltmeter reading is 2.4 V calculating: the resistance of the lamp; the resistance of R_1. Compare the brightness of the lamp when both switches are open as in (a) and when only switch Si is closed. Give a quantitative explanation. Compare the brightness of the lamp when both switches are open as in (a) and when both switches S_1 and S_2 are closed. Give a quantitative explanation. For R_2 = 4 ohm, if switch Si is opened but switch S_2 is closed, what is ammeter reading? What is voltmeter reading?

Explanation / Answer

part a:

let resistance of lamp be R ohms.

as R1 and R are in series, current through R=current through R1=reading of ammeter=0.6 A

then R=voltage across R/current through R

=2.4/0.6=4 ohms

as R1 and R in series,

total voltage=voltage across R1+voltage across R

==>voltage across R1=6-2.4=3.6 volts

then R=voltage across R/current through R=3.6/0.6=6 ohms

part b:

brightness is directly proportional to power consumed by the bulb.

as power=current^2*resistance

higher the current through the bulb, higher is the brightness.

when both switches are open, current through lamp is 0.6 A

when only S1 is closed,R1 is shorted.

net resistance in the circuit=R=4 ohms

current=voltage/resistance=6/4=1.5 A

so brightness when both switches are open/ brightness when only S1 is closed

=0.6^2/1.5^2

=0.16

part c:

when S1 and S2 are closed, R1 is shorted.

R2 is connected in parallel with R.

so resistance becomes R*R2/(R+R2) which is less than R

hence current increases and brightness increases.

part d:

when S1 is opened and S2 is closed,

R2 and R are in parallel.

equivalent resistance=R2*R/(R2+R)=4*4/(4+4)=2 ohms

this is in series with R1.

so net resistance in the circuit=2+6=8 ohms

current =6/8=0.75 A

voltage across R=voltage aceoss 2 ohms=2*0.75=1.5 volts

so ammeter reading=0.75 A

voltmeter reading=1.5 volts

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