A battery has an internal resistance of 0.42. A number of identical light bulbs, each with a resistance of 31.500, are connected in parallel across the battery terminals. The terminal voltage of the battery is observed to be one-half the emf of the battery. How many bulbs are connected?

Question

A battery has an internal resistance of 0.42. A number of identical light bulbs, each with a resistance of 31.500, are connected in parallel across the battery terminals. The terminal voltage of the battery is observed to be one-half the emf of the battery. How many bulbs are connected?

Answer 1

well, I.42=31.5/n I

n= 31.5/.42

Answer 2

To find out how many light bulbs are connected in parallel, we can use the concept of equivalent resistance. The equivalent resistance of a set of resistors connected in parallel is given by the formula:

1/Req = 1/R1 + 1/R2 + 1/R3 + ...

In this case, since all the light bulbs are identical, we can represent the equivalent resistance as:

1/Req = 1/R + 1/R + 1/R + ...

Where R is the resistance of one light bulb.

Given that the internal resistance of the battery is 0.42 and the terminal voltage is one-half the electromotive force (emf) of the battery, we can use the equation for terminal voltage:

V = emf - I * r

Where V is the terminal voltage, emf is the electromotive force, I is the current flowing through the circuit, and r is the internal resistance of the battery.

Since the equivalent resistance of the light bulbs is connected in parallel, the current flowing through each light bulb will be the same. Let's assume this current is I.

Now, we can calculate the terminal voltage (V) in terms of the emf of the battery as follows:

V = emf - I * r

Given that V = emf/2, we can write:

emf/2 = emf - I * r

emf/2 - emf = -I * r

emf(1/2 - 1) = -I * r

emf/2 - emf = -I * r

emf/2 - 2emf/2 = -I * r

-emf/2 = -I * r

emf/2 = I * r

Now we can substitute the current (I) with the emf divided by the equivalent resistance (Req) calculated from the equation for equivalent resistance:

emf/2 = (emf/Req) * r

emf * Req/2 = emf * r

Req/2 = r

Req = 2r

Now, we can substitute the equivalent resistance (Req) with 2 times the resistance of one light bulb (2R):

2R = 2r

R = r

So, the resistance of one light bulb (R) is equal to the internal resistance of the battery (r).

Thus, we can conclude that the number of light bulbs connected in parallel is equal to 1.

A battery has an internal resistance of 0.42. A number of identical light bulbs, each with a resistance of 31.500, are connected in parallel across the battery terminals. The terminal voltage of the battery is observed to be one-half the emf of the battery. How many bulbs are connected?

well, I*.42=31.5/n * I

To find out how many light bulbs are connected in parallel, we can use the concept of equivalent resistance. The equivalent resistance of a set of resistors connected in parallel is given by the formula:

well, I.42=31.5/n I