Consider the circuit shown in the figure (Figure 1). Suppose the four resistors
ID: 1439216 • Letter: C
Question
Consider the circuit shown in the figure (Figure 1). Suppose the four resistors in this circuit have the values R_1 = 10 ohm, R_2 = 7.5 ohm, R_3 = 8.0 ohm, and R_4 = 15 ohm, and that the emf of the battery is epsilon = 18 V. Find the current through each resistor using the rules for series and parallel resistors. Express your answers using two significant figures separated by commas. Find the current through each resistor using Kirchhoff's rules. Express your answers using two significant figures separated by commas.Explanation / Answer
here,
R1 = 10 ohm , R2 = 7.5 ohm
R3 = 8 ohm
R4 = 15 ohm
A)
Re = ( R2 + R4) * (R3)/( R2 +R4 + R3)
Re = ( 15+7.5) *(8)/(15+7.5+8)
Re = 5.9 ohm
Req= Re + R1
Req = 15.9 ohm
current through R1 , I1 = E/Req
I1 = 18/15.9 = 1.13 A
voltage drop across AB , Vab = E - i1*R1
Vab = 18 - 1.13 *10
Vab = 6.68 V
current through R3 , I3 = Vab/R3 = 6.68/8 = 0.84 A
current through R2 and R4 , I2 = I4 = Vab/(R2+R4)
I2 = I4= 0.3 A
B)
let the current be i1 , i2 and i3
using KVL in left loop
R1*i1 + i3*R3 + E = 0
10 * i1 + 8 * i3 + 18 = 0 ...(1)
and using KVL in right loop
i2*r4 * i2*r2 - i3*r3 = 0
i2*22.5 - 8 * i3 = 0 ...(2)
and using KCL
i1 = i2 +i3 ...(3)
from equation (1) , (2) and (3)
i1 = 1.13 A , i2 = i4 = 0.3 A , i3 = 0.84 A