Two bulbs are connected in parallel across a source of emf EMF = 10.0V with a negligible internal resistance. One bulb has a resistance of 3.0 Omega , and the other is 2.5 Omega . A resistor R is connected in the circuit in series with the two bulbs.

What is the current through each individual bulb? Let I1 be the current through the bulb of resistance 3.0 Omega and I2 the current through the bulb of resistance 2.5 Omega?

To find the current through each individual bulb, we can use Ohm's Law and analyze the circuit using the concept of parallel and series connections.

First, let's calculate the total resistance of the two bulbs connected in parallel. In a parallel circuit, the total resistance (R_parallel) is given by the formula:

1/R_parallel = 1/R1 + 1/R2

where R1 and R2 are the resistances of the individual bulbs. Plugging in the values:

1/R_parallel = 1/3.0 + 1/2.5

1/R_parallel = (2.5 + 3.0)/(3.0 * 2.5)

1/R_parallel = 5.5/7.5

R_parallel = 7.5/5.5

R_parallel = 1.3636...

Now, we can calculate the total current (I_total) flowing through the circuit. The total current is equal to the emf (EMF) divided by the total resistance (R_total):

I_total = EMF / R_total

Since there is negligible internal resistance, the total resistance (R_total) is equal to the resistance (R_parallel) of the bulbs added to the resistance (R) of the external resistor:

R_total = R_parallel + R

Now, plug in the given values of EMF and R_parallel to find I_total.

I_total = 10.0V / (R_parallel + R)

Next, we can find the individual currents I1 and I2 through each bulb using the concept of current division. In a parallel circuit, the current divides among the branches in inverse proportion to the resistance:

I1 = I_total * (R_parallel / (R_parallel + R))

I2 = I_total * (R / (R_parallel + R))

Substitute the values of I_total, R_parallel, and R to find the currents I1 and I2.

I1 = I_total * (R_parallel / (R_parallel + R))

I2 = I_total * (R / (R_parallel + R))

Now you can calculate I1 and I2 using the above expressions.

2.4/3=.8 A

2.4/2.5=.96 A