all the problems please. Thank you! Consider a circuit shown in the figure. Igno

Question

all the problems please. Thank you!

Consider a circuit shown in the figure. Ignore the internal resistances of the batteries. E_1 = 12 V E_2 = 48 V R_1 = 4 ohm R_2 = 6 ohm R_3 = 5 ohm. Express the current I_1 going through resistor R_1 in terms of the currents I_2 and I_3 going through resistors R_2 and R_5. Use the direction of the currents as specified in the figure. Write the equation of potential change in loop EBAF in terms of the circuit elements. Write the equation of potential change in loop DCAF in terms of the circuit elements. Solve the three equations to get I_3. Calculate the numerical value of I_3 in A. Calculate the numerical value of I_2 in A. Calculate the numerical value of I_1 in A.

Explanation / Answer

Here ,

part a)

Using KCL at node E

I1 - I2 - I3 = 0   

part b)

for the potential change in loop EBAF

E1 - I1 * R1 - R3 * I3 = 0

part c)

the potential change in loop DCAF

- E2 + I2 * R2 - I3 * R3 = 0

part d)

I1 - I2 - I3 = 0

12 - 4 I1 - 5 * I3 = 0

-48 + 6 * I2 - 5 I3 = 0

solving

I1 = 5.07 A

I2 = 6.65 A

I3 = -1.62 A

the currents I3 is -1.62 A

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