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Question Video: Calculating Total Current in a Parallel Circuit Physics • 9th Grade

What is the total current through the circuit shown? Give your answer to two decimal places.

02:28

Video Transcript

What is the total current through the circuit shown? Give your answer to two decimal places.

We have a circuit that shows three resistors in parallel, and we want to find the total current through the circuit. To calculate the current through the circuit, we can convert the three resistors in parallel into a single equivalent resistor, which we’ll call 𝑅 total. Then, we can use Ohm’s law to find the current in this equivalent circuit.

Recall that for any number 𝑁 of resistors in parallel, the total equivalent resistance equals the inverse of the quantity one over 𝑅 one plus one over 𝑅 two plus dot dot dot plus one over 𝑅 sub 𝑁. So, for this circuit, we can replace the three resistors that are connected in parallel with a single equivalent resistor, which will have a resistance 𝑅 total equal to the inverse of the quantity one over 𝑅 one plus one over 𝑅 two plus one over 𝑅 three. By substituting in the values for the three resistors, 6.5 ohms, 3.5 ohms, and 9.5 ohms, we find that 𝑅 total equals 1.8354 and so on ohms.

We can now use Ohm’s law across the single resistor 𝑅 total to find the value of the current in the equivalent circuit. Recall that Ohm’s law can be written as 𝑉 equals 𝐼 times 𝑅, where 𝑉 is the potential difference, 𝐼 is the current, and 𝑅 is the resistance. In this question, we’re trying to find the current in the circuit, 𝐼. So, we need to rearrange Ohm’s law to make 𝐼 the subject. This can be done by dividing both sides of the equation by 𝑅. This gets us 𝐼 equals 𝑉 divided by 𝑅.

We are given a cell which is providing a potential difference of 6.5 volts across the circuit. So, by substituting in this value and the resistance we just calculated, we can use Ohm’s law to find the current across the single resistor. The current we’ve calculated across the single resistor is equal to the total current through the original circuit, which is what the question has asked us to find.

The final bit we need to complete this question is to give the answer to two decimal places. We will take the numbers before the decimal place and the three numbers after the decimal place to get 3.541 amperes. Then, we look at the third number after the decimal place to see if we need to round down or round up. We see that the third number after the decimal place is one, so we can round this down to zero, which leaves the answer to be 3.54 amperes. Hence, the total current through the circuit is 3.54 amperes.

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