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we are asked how does the current going through r1 so this resistor when the switch is open this switch compared to the current through r1 when the switch is closed pause this video and see if you can figure that out alright so let's just think about the two scenarios so we could view the current as this right over here this current that we care about we could either measure it there or you could measure it right over there and let's first think about the scenario where the switch is open so our current when our switch is open is going to be equal to the voltage across the resistors and that's going to be our 12 volts 12 volts divided by the equivalent resistance of these resistors when the switch is open essentially we just have r1 and r2 in series and so this is just going to be r1 plus r2 if you have two resistors in series their equivalent resistance is just the sum of their resistances fair enough now let's think about the situation where the switch is closed closed so here our current at this point of our circuit or the current going through r1 so I so closed is once again it's going to be equal to 12 volts the voltage across the resistors but we're good what are we going to divide by now when we close the switch what happens well these lines where we see no resistors in circuit diagrams that's assumed to be resistance 'less so all of the current will actually flow that way so by closing this switch you're essentially removing r2 from the circuit the current will just go through r1 and then follow the path of least resistance literally and so in this situation our current is going to be 12 volts divided by you essentially just have 1 resistance divided by r1 so when you closed the circuit you've essentially taken a resistor out and so if you took a resistor out you're going to increase the current so you could just write it as the current when the switch is open is going to be less than is going to be less than the current when the switch is closed once again why is that well just look at the denominators here when the switch is open you're dividing by a larger number then when the switch is closed or another way of thinking about it when the switch is open the r2 resistance is factored in when the switch is closed the r2 resistance essentially becomes a non-factor and you have less resistance which would mean you out have higher current

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