Consider a circuit with 2 identical bulbs wired in parallel. If we add another bulb in parallel,
explain the changes to the measured values of the circuit properties. (Be explicit – for
example, you could say the value doubles, but don’t just say the quantity increases.)
a. Voltage.
b. Current.
c. Equivalent resistance.
d. Power of the circuit.
e. The brightness of each bulb.
Assuming battery or power line resistance is low the voltage will not change
However the current now has a third path to follow so the current will increase. If each resistor is R original resistance was R/2
new resistance = Rnew
Rnew = (1/3) R
i original = V/(R/2) = 2 V/R
i new = 3/2 of current with just 2 resistors in parallel = 3V/R
original power = V (2 V/R) = 2 V^2/R
end power = V(3 V/R) = 3 V^2/R
Voltage is the same for each bulb of course, until you blow the fuse :)
To understand the changes in the measured values of circuit properties when adding another bulb in parallel, let's go through each property one by one:
a. Voltage:
When bulbs are wired in parallel, each bulb gets the same voltage. So, if we add another bulb in parallel, the voltage across each bulb remains the same. It does not change with the addition of more bulbs.
b. Current:
When bulbs are wired in parallel, the total current is divided among the bulbs. So, if we add another bulb in parallel, the total current in the circuit increases. It doubles when the number of bulbs doubles and so on. Each bulb receives an equal share of the total current.
c. Equivalent resistance:
When bulbs are wired in parallel, the equivalent resistance decreases. Adding more bulbs in parallel decreases the total resistance. In fact, the reciprocal of the equivalent resistance is equal to the sum of reciprocals of individual resistances. So, as more bulbs are added in parallel, the equivalent resistance decreases.
d. Power of the circuit:
The power of the circuit is calculated by multiplying the voltage and current. Since the voltage across each bulb remains the same, and the current through each bulb increases when more bulbs are added, the power of the circuit increases when another bulb is added in parallel. It doubles when the number of bulbs doubles, and so on.
e. Brightness of each bulb:
In a parallel circuit, each bulb is independent and unaffected by the others. So, with the addition of another bulb, the brightness of each bulb remains the same. The total current is divided among the bulbs, but the voltage across each bulb does not change. Therefore, adding more bulbs in parallel does not affect the brightness of the individual bulbs.
To summarize:
a. Voltage remains the same.
b. Current increases, doubling when the number of bulbs doubles.
c. Equivalent resistance decreases.
d. Power of the circuit increases, doubling when the number of bulbs doubles.
e. Brightness of each bulb remains the same.