Consider the circuit shown in the figure(Figure 1). Suppose the four resistors i
ID: 1643244 • Letter: C
Question
Consider the circuit shown in the figure(Figure 1). Suppose the four resistors in this circuit have the values R_1 = 13 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
Remember:
For series combination
Req = R1 + R2 + R3 +...............
for parallel combination
1/Req = 1/R1 + 1/R2 + 1/R3 + ............
for 2 resistors in parallel it will be
Req = R1*R2/(R1+R2)
Using this Information:
Rs = R2 + R4 = 7.5 + 15 = 22.5 ohm
Rp = 8*22.5/30.5 = 5.9 ohm
Req = 5.9 + 13 = 18.9 ohm
ieq = V/Req = 18/18.9 = 0.952 Amp.
Now remember in resistors parallel combination voltage distribution in each part will be same and in series combination current distribution in each resistor will be same.
Current in R1 = ieq = i1 = 0.952 Amp.
Current in Rp = ieq = ip = 0.952 Amp.
Vp = ip*Rp = 0.952*5.9 = 5.617 V
V3 = Vp = 5.617 V
i3 = V3/R3 = 5.617/8 = 0.702 Amp.
is = ieq - i3 = 0.952 - 0.702 = 0.25 Amp.
i2 = i4 = is = 0.25 Amp.
B.
Now using krchoff's law:
current in R1 = i1,
current in R3 = i3,
current in R2 = i2,
kirchoff's current law:
i1 = i2 + i3
kirchoff's voltage in left loop:
V = i3*R3 + i1*R1
18 = 8*i3 + 13*i1
kirchoff's voltage in right loop:
0 = i3*R3 - (R2 + R4)*i2
i3*8 = (7.5 + 15)*i2
i3 = i2*(22.5/8)
i3 = 2.812*i2
i1 = i2 + i3 = i2 + 2.812*i2
i1 = 3.812*i2
18 = 8*i3 + 13*i1
18 = 8*2.812*i2 + 13*3.812*i2
18 = 72.052*i2
i2 = 18/72.052 = 0.249
i1 = 3.812*0.249 = 0.949
i3 = 2.812*0.249 = 0.700