Physics - circuits

By the use of maths, assume the resistance of the bulbs and resistor are the same, r.

The voltage supplied is V, the current across the circuit (L1 and L2) is I before the switch S is closed.

V=IR=2Ir

When S is closed, the resistance of the circuit become r+(1/r+1/r)^(-1)=3r/2

The new current In = V/R=2/3 V/r = 4/3 I.
The current pass thought L1 will increase.
While at the same time, current passing thought L2 will be (4/3 I )/2=2/3 I. Smaller then before.

As a result, L1 will be brighter, L2 will be dimmer. It is true for all resistance of the resistor. the present of the resistor will decrease the equivalent resistor of the whole circuit, make the current passing thought the circuit increase. At the same time, it will draw out current passing thought L2.

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assume both resistance of the lamps are same = R

resistance of the unknown resistor = r

when switch is open , current pass through both lamps is V / 2*R,
power consume at each lamp is V^2 / 4*R

case 1 : r ~ 0, no current pass L1, total resitance is half, current pass L2 doubled (2 times brighter)

case 2 : r ~ infinity, no current pass r, same condition as switch open

case 3 : r = R, total resistance is smaller, current pass L2 larger, current pass L1 lesser ( L2 brighter, L1 dimmer)

conclusion : when switch closed,
L1 brightness : dark to same brightness as before;
L2 bightness : 2 times brighter to same brightness as before
as r change from 0 to infinity

2008-10-27 18:08:51 補充：
Sorry, make a mistake in notation in L1, L2
Pls change L1 to L2, L2 to L1 in above answer.

When the switch S is closed, the total load resistance of the circuit increases thus decreasing the total load current from the battery, both lamps are dimmer than before. But the resistor by-passes part of the current from the lamp L2, meaning the current thru the lamp L2 is smaller than lamp L1. So the end result is lamp L1 is still brighter than L2 comparatively even though both lamps are dimmer than when the switch S was opened.

Answer: brightness of both lamps are lower, but lamp L2's brightness is much lower.

圖中電阻器,電阻=燈泡的電阻??
如果唔係就要分CASE