Question

17. Alyssa just bought a new set of string lights for her bedroom. She decided to use the lights to outline her mirror. The lights are on a series circuit. If Alyssa were to buy more lights so that they can go all around her bedroom, what will happen to following quantities?:
a. The resistance of the entire circuit will (increase/decrease).
b. The current through each bulb will (increase/decrease).
c. The voltage available to each bulb will (increase/decrease).

Answer 1

a. The resistance will increase

b. The current will decrease

c. The voltage through each bulb will

Explanation:

a. For a series of resistors, the equivalent resistance is given by

$R=R_1+R_2+...+R_n$

so, we see that adding more resistors in series, will increase the total resistance.

b. In a series circuit, the current through each bulb is the same for each bulb, and it is equal to the current flowing in the circuit, which is given by Ohm's law

$I=\frac{V}{R}$

where V is the voltage supplied by the battery and R the total resistance of the circuit. Since the voltage provided by the battery, V, does not change, while the total resistance R increases, the current I will increase.

c. The voltage through each bulb is given by

$V=R_i I$

where R_i is the resistance of the individual resistor and I is the current. Since the value of R_i does not change, while I (the current) has decreased, the voltage available to each bulb, V, will decrease.