hello everyone hope you guys are doing well so here we have an electricity question and the first question says determine the value of v1 so the first thing i would want you to realize is that v1 is the volt meter that is measuring this parallel combination over here and what we should remember is that voltage in parallel is the same and so if you had to look at this branch over here you should realize that we've got the current which is 0.6 amps and then we've got the 4 ohm resistor so we could use v equals to i times r just for that little branch over there and so that's going to be equal to 0.6 multiplied by 4 and that's going to give us 2.4 volts and so that will be the voltage for v1 which what it also means is that that's the voltage across this branch and it's also the voltage across this branch because why voltage in parallel is the same the next question says determine the value of a1 so a1 is the current flowing in the main part of the circuit so what we could do here is we must realize that the electricity will flow out of or the conventional current flows out of the positive and then it gets to this part over here and then it splits some of the electricity will go down this branch while the remaining electricity would go down here we already know that zero comma six amps is going through this branch so what we would need to do now is work out how much electricity is flowing through this branch we could then add those two together and that would tell us how much current is flowing in the main part of the circuit so we already know that in this part of the circuit over here we know that the voltage is two comma four volts 2.4 volts because we said voltage in parallel is the same and so only looking at these two numbers here i can use i equals v over r and that will give us a voltage of we know the voltage is 2.4 the resistance is 6. and so if we're to work that out we end up with 0 comma four amps so we have zero comma six amps flowing in this branch and we have zero comma four amps flowing through that branch and so if we add them up we can then say that a1 will be equal to 0.6 plus 0.4 and so that will be 1 amp the last question says determine the emf of the battery so the most easy way to do this for a situation like this would just be to use the emf formula which goes emf is equal to i bracket big r plus small r and so we want to calculate the emf we already know the current flowing in the main part of the circuit remember that that current there is the main part of the circuit which is the one amp that we've just calculated now we're gonna have to know small r now remember the small r is the internal resistance of the battery so that's 0.8 but the big r is all of the resistors in the external part of the circuit now the external part would be everything outside the battery so it would be these two together and this one so kevin does that mean we're just gonna add them all up well it depends these two over here are in parallel so we don't add them up we don't say 6 plus 4 instead we add them up using the parallel formula which goes like this 1 over r parallel is equal to 1 over r1 plus 1 over r2 so we're going to go add that up first so 1 over 6 plus 1 over 4 you'll then just go add those two numbers together and no it's not going to be 1 over 10 be careful there you're just going to add them up on your calculator and that gives you 5 over 12. you can then flip this upside down and you flip this one upside down and so r parallel is equal to 12 over 5 which is the same as 2 comma 4 ohms there we go and then we can add that 2 comma 4 to this 5 comma 8 because what we've done is we've taken these two we can think of we've taken those two away and we've turned them into a single resistor of two comma four and so now it's that two comma four will be in series with that five comma eight and so we just add them together now so r is going to be 2 comma 4 plus 5.8 and that will be 8.2 ohms and so that is the r that we can use in this part of the formula over there and so if we had to go work this all out we should find that the emf of the battery is 9 volts awesome that's done for this question see you in the next one