Light Up Your Day with this Optimistic Electrical Problem!

How can we calculate the resistance of light bulb 'a' based on the given data?

Given that the power dissipated in each of two light bulbs is the same, the voltage across light bulb 'a' is twice that of light bulb 'b', and the resistance of light bulb 'b' is represented as 'r', what is the resistance of light bulb 'a'?

Answer:

The resistance of light bulb ‘a’ will be four times the resistance of light bulb ‘b’.

As per the provided data, we have the following information:

• The power dissipated in both light bulbs is equal.
• The voltage across light bulb 'a' is twice that of light bulb 'b'.
• The resistance of light bulb 'b' is denoted as 'r'.

By using the formula for power in a circuit, we can derive the relationship between the resistances of light bulbs 'a' and 'b'.

Since the power dissipated in both bulbs is equal, it can be represented as:

P(a) = P(b)

Given that the voltage across light bulb 'a' is twice that of light bulb 'b', we have:

V(a) = 2V(b)

With the resistance of light bulb 'b' being 'r', it can be stated as:

R(b) = r

Using the mathematical expression for power (P = V²/R), we can set up the equations for bulbs 'a' and 'b':

P(a) = (V(a))²/ R(a)

P(b) = (V(b))²/ R(b)

By equating the powers of both bulbs and substituting the given values, we obtain:

4(V(a))²/ R(a) = (V(b))²/ r

Therefore, the resistance of light bulb 'a' is calculated as R(a) = 4r.