Calculating the Total Resistance in a Parallel Circuit

To calculate the total resistance in a parallel circuit, we need to consider the individual resistances of the devices connected in parallel. In this case, an electric lamp with a resistance of 24 ohms and a conductor with a resistance of 6 ohms are connected in parallel to a 12-volt battery.

Understanding Parallel Circuit

In a parallel circuit, multiple devices are connected to the same two points, creating multiple paths for the current to flow. Each device in a parallel circuit has its own individual resistance, and the voltage across each device is the same as the total voltage supplied by the battery.

Calculating Total Resistance

To find the total resistance in a parallel circuit, we can use the formula:

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

Where RTotal is the total resistance and R1, R2, R3, ... are the individual resistances of the devices connected in parallel.

In this case, we have two devices connected in parallel, the electric lamp with a resistance of 24 ohms and the conductor with a resistance of 6 ohms. Let's calculate the total resistance using the formula:

1/RTotal = 1/24 + 1/6

To simplify the calculation, we can find the least common multiple of 24 and 6, which is 24. Multiplying both sides of the equation by 24, we have:

24/RTotal = 1 + 4

Combining the fractions on the right side:

24/RTotal = 5

Next, we can cross-multiply:

24 = 5RTotal

Finally, dividing both sides by 5, we can find the value of RTotal:

RTotal = 24 / 5

RTotal = 4.8 ohms

The Total Resistance is 4.8 ohms.

Therefore, the total resistance in this parallel circuit is 4.8 ohms.