The required concepts to solve these questions are effective resistance of the combinations of the resistor, power dissipated by the bulbs and potential across the bulbs.
Firstly, solve the circuit by using series and parallel combination of the resistor, calculate the current in the circuit and calculate power dissipated by the bulbs. Rank the bulbs based on the brightest to dimmest.
The expression for equivalent resistance for series combination of resistors is,
Here, is the equivalent resistance of the bulb in series, is the resistance of the bulb and is the resistance of the other bulb.
The expression for parallel combination of resistors is,
Here, is the equivalent resistance of the bulb in parallel.
The expression for circuit in the circuit is.
Here, is the resistance and is the potential.
The expression for power dissipated by bulb is,
Here, is the current in the circuit and is the resistance.
Diagram of bulbs is given as,
For bulb A and B.
Bulb A and B are connected in parallel. The expression for equivalent resistance for parallel connection is,
Substitute for and in the above equation.
…… (1)
Bulb D and E are connected in series. The expression for equivalent resistance of bulb D and E connected in series is,
Substitute for and in the above equation.
…… (2)
Bulb DE is parallel with bulb C. The expression for equivalent resistance for parallel connection is,
Substitute for and for in the above equation.
…… (3)
The expression for current in the circuit is,
Here, is the current through the bulb A and B, is the potential and is the resistance of bulb AB.
From the equation (1), .
Substitute for in the above equation.
…… (4)
A and B have equal resistance and they are connected in parallel so current divides equally.
Thus,
and
.
The expression for current in the circuit is,
Here, is the current through the bulb D and E.
From the equation (2), .
Substitute for in the above equation.
…… (5)
The expression for current in the circuit is,
Here, is the current through the bulb C, D and E.
From the equation (3), .
Substitute for in the above equation.
…… (6)
The expression for power dissipated by bulb A is,
Substitute for and for in above equation.
Bulb A and B has same resistance and same current. They dissipate equal power. So
. …… (7)
Substitute for in the above equation.
The expression for power dissipated by bulb C is,
There are three bulbs in that bulb C is in parallel with bulb DE. of current pass through bulb C and of current pass through bulb DE.
From the equation (6),
Substitute for and for in the above equation.
Substitute for in above equation.
Bulb D and E are connected in the series so power dissipated in the D and E are same.
…… (8)
The expression for power dissipated by bulb D is,
Substitute for and for in the above equation.
Substitute for in equation (8).
Compare the power of bulbs. Power dissipated by bulb A, B, C, D, E are , , , , .
Rank of the bulbs based on their brightness.
Bulb C has brightest than A and B which are equal and D and E are dimmest.
Ans:Rank of the bulbs based on their brightness are .
Part A Consider a circuit containing five identical light bulbs and an ideal battery. Assume that...
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