### 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 weβll call π
total. Then, we can use Ohmβs law to find
the current in this equivalent circuit.

Recall that for any number π of
resistors in parallel, the total equivalent resistance equals the inverse of the
quantity one over π
one plus one over π
two plus dot dot dot plus one over π
sub
π. 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 π
total equal to the inverse of the quantity
one over π
one plus one over π
two plus one over π
three. By substituting in the values for
the three resistors, 6.5 ohms, 3.5 ohms, and 9.5 ohms, we find that π
total equals
1.8354 and so on ohms.

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

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 Ohmβs law to find the current
across the single resistor. The current weβve 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.