Use Kirchhoff\'s rules to find the current in each of the three resistors in the

Question

Use Kirchhoff's rules to find the current in each of the three resistors in the circuit shown in the picture. Also, calculate the voltage drop across all three resistors. PLEASE show your work. (Note: there is a typo baterries should read 4V and 12 V and the middle resistor is 18ohm)

Explanation / Answer

let i1 be current in upper loop in clockwise direction.............................................................. let i2 be current in lower loop in anticlockwise direction............................................... now current through 16 ohm resistor is i1,through 8 ohm resistor is i2, through 18 ohm resistor is i1+i2................................applying kirhoff law for upper loop we get............. 12-18(i1+i2)-16i1-4=0.......=>2i1+18i2=8.....=>i1+9i2=4.... let it be equation 1.......... now applying kirchoff law for lower loop............ 12-18(i1+i2)-8i2=0.........=>9i1+13i2=6... let it be equation 2...................solving equation 1 and equation 2 we get..i1=0.03 ampere and i2=0.44 ampere....... so current through 16 ohm resistor is 0.03 ampere... current through 8 ohm resistor is 0.44 ampere......... current through 18 ohm resistor is 0.44+0.03=0.47 ampere......

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