In the circuit shown what is the value of current i1 if...

Transcript

00:02 Hello students, so we are provided with the given circuit here.

00:05 In this circuit we have 2 emfs e1 is equal to 12 volts and e2 is equal to 6 volts and we have 3 resistances and the currents provided and in this question we need to find out what is the value of current i1 here.

00:18 So if this is the point of node p so we can say that add node point p at node point p we have that i 1 is equal to i2 plus i3 so from here we can say that i 3 is simply equal to i 1 minus i 2 now let us take let us apply the kchof's voltage low that is also called the kviel law to the first loop that is loop a b cd so we can see here applying kitchf's voltage law to loop ab cd and we are going in the anti -clockwise direction we get that we get so this is so what does kichof's voltage law say is that in a closed loop the sum of all the voltages is equal to zero and for a resistance are current i flowing through it the voltage is equal to i r okay so we have for the loop a b cd the voltage law would be minus of hundred multiplied by i y then through the 2 -home resistance we have minus of 10 multiplied by i 2 is equal to sorry plus 12 is equal to 0 or what we can say is that 12 is equal to 100 i 1 plus 10 i 2 now again we're going to apply kitchf's voltage law but now we are going to apply it again we're going in the anticlockwise direction but we'll apply it on the loop b c e f so what we can see here now is that applying kvl to loop b c ef we get so from here we get that minus of 12 volts plus 10 multiplied by i 2 minus of 5 i 3 and i 3 as we and the current flowing through see if we see the figure here if we see the figure here then we can see that the current i3 is flowing through the 5 -arm resistance and i3 as we discussed is i 1 minus i 2 so we'll write 5 of i 1 minus i 2 minus of 6 is equal to 0 so this implies that 18 is equal to 10 i 2 minus of 5 i 1 minus i 2 so this is equation 2 this is equation 3 and the node rule that is equation 1 now we'll solve we'll simplify equation number 3 first so from here we have simplifying equation 3 we get simplifying equation 3 we get that 18 is equal to 10 i 2 minus of 5 i 1 plus of 5 i2 so this implies that 15 i2 minus of 5 i 1 is equal to 18 and in equation 2 we had equation number 2 we had 100 i 1 plus 10 i 2 plus 10 i 2 is equal to 12 since we need to find out the value of i 1 in this equation so we are going to cancel the i 2 components of both the equations so we'll just multiply this with 15 on each side so if we multiply 10 to this of the equation and then we multiply 15 to this side of the equation what we what do we get so it's 150 i2 minus 50 i 1 is equal to 180 and this is again 150 i 2 150 i 2 150 i 2 and this is plus 1500 plus 1500 i1 is equal to 180 now if we subtract this equation so this gets cancelled and we have here so this is also minus here so this becomes minus so we have minus of 1 150 i 1 is equal to 0 this implies that i 1 is equal to 0 so this is the value of i 1 current that is equal to 0 so this is the value of i 1 current that is flowing through the given now we already found out the value of the current i1 here so using the value of current i1 we can then find out the value of the other two currents i 2 and i 3 in the circuit so from equation equation number 3 we have equation 3 we had 15 i2 minus 5 i 1 is equal to 18 so since i 1 is equal to 0 i 1 tends to 0 so we have 15 i 2 i 2 is equal to 18 or we can say that i 2 is equal to 18 divided by 15 ampere so if we make this calculation dividing it by 3 we get that i 2 is equal to 6 divided by 5 that is equal to 1 .2 ampere and now we're putting the values of i 1 and i 2 into the node equation that is equation 1 so we get here putting values of i 1 and i2 we get so we had the original equation equation one that is i1 is equal to i2 plus i 3 that is 0 is equal to 1 .1 .2 ampere plus i 3 or we can say that i 3 is equal to minus of 1 .2 ampere so the negative sign in this final value of i 3 indicates that the the current i3 is flowing, the current i3 is flowing opposite to i2...

Question

In the circuit shown, what is the value of current (I1), if R1=100 Ohms, R2=10 Ohms, R3=5 Ohms, E1=12 Volts and E2=6 Volts? What is the value of current I2? What is the value of current I3?

Question

In the circuit shown, what is the value of current (I1), if R1=100 Ohms, R2=10 Ohms, R3=5 Ohms, E1=12 Volts and E2=6 Volts? What is the value of current I2? What is the value of current I3?

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