Consider the circuit shown in (Figure 1). The batteries have emfs of E1=9.0V and E2=12.0V and the resistors have values of R 1=26?, R 2=62?, and R 3=37?.
A) Determine the magnitudes of the currents in each resistor shown in the figure. Ignore internal resistance of the batteries.
Express your answers using two significant figures separated by commas.
B) Determine the magnitudes of the currents in each resistor shown in the figure. Assume that each battery has internal resistance r = 1.0 ?.
Express your answers using two significant figures separated by commas.
Solution
here,
E1 = 9 V , E2 = 12 V
R1 = 26 ohm R2 = 62 ohm
R3 = 37 ohm
let the current through each resistors be i1 , i2 and i3
using KVL in the upper loop
R1 * i1 + R2 * i2 = E1
26 * i1 + 62 * i2 = 9 ...(1)
using KVL in the lower loop
R3 * i3 + R2 * i2 = E2
37 * i3 + 62 * ( i2) = 12 ....(2)
using KCL
i2 = i1 + i3 ....(3)
from (1) , (2) and (3)
i1 = 0.03 A
i2 = 0.13 A
i3 = 0.102 A
b)
when r = 1 ohm
let the current through each resistors be i1 , i2 and i3
using KVL in the upper loop
(R1 + r ) * i1 + R2 * i2 = E1
27 * i1 + 62 * i2 = 9 ...(1)
using KVL in the lower loop
(R3 + r) * i3 + R2 * i2 = E2
38 * i3 + 62 * ( i2) = 12 ....(2)
using KCL
i2 = i1 + i3 ....(3)
from (1) , (2) and (3)
i1 = 0.03 A
i2 = 0.132 A
i3 = 0.108 A
.
Consider the circuit shown in (Figure 1)- The batteries have emfs of E.docx
1. Consider the circuit shown in (Figure 1). The batteries have emfs of E1=9.0V and E2=12.0V and
the resistors have values of R 1=26?, R 2=62?, and R 3=37?.
A) Determine the magnitudes of the currents in each resistor shown in the figure. Ignore internal
resistance of the batteries.
Express your answers using two significant figures separated by commas.
B) Determine the magnitudes of the currents in each resistor shown in the figure. Assume that
each battery has internal resistance r = 1.0 ?.
Express your answers using two significant figures separated by commas.
Solution
here,
E1 = 9 V , E2 = 12 V
R1 = 26 ohm R2 = 62 ohm
R3 = 37 ohm
let the current through each resistors be i1 , i2 and i3
using KVL in the upper loop
R1 * i1 + R2 * i2 = E1
26 * i1 + 62 * i2 = 9 ...(1)
using KVL in the lower loop
R3 * i3 + R2 * i2 = E2
37 * i3 + 62 * ( i2) = 12 ....(2)
2. using KCL
i2 = i1 + i3 ....(3)
from (1) , (2) and (3)
i1 = 0.03 A
i2 = 0.13 A
i3 = 0.102 A
b)
when r = 1 ohm
let the current through each resistors be i1 , i2 and i3
using KVL in the upper loop
(R1 + r ) * i1 + R2 * i2 = E1
27 * i1 + 62 * i2 = 9 ...(1)
using KVL in the lower loop
(R3 + r) * i3 + R2 * i2 = E2
38 * i3 + 62 * ( i2) = 12 ....(2)
using KCL
i2 = i1 + i3 ....(3)
from (1) , (2) and (3)
i1 = 0.03 A
i2 = 0.132 A
i3 = 0.108 A
