In the circuit shown in figure, `E_1 and E_2` are tow ideal sources of unknown emfs. Some currents are shown. Potential differences appearing across resistance is `V_A - V_B = 10V.`

Options

A. The current in the `4.00 Omega` resistor is 5 A.
B. The unknown emf `E_1 is 36V. `
C. The unknown emf `E_2 is 54V.`
D. The resistance R is equal to `9Omega`.

Answer

A, B, C, D

Explanation

a., b., c., d.

After redrawing the circuit
.
a. `I_4 = 5A`
b. From loop (1),
`-8(3) + E_1 - 4(3) = 0 or E_1 = 36V`
From loop (2),
`+4(5) + 5(2) - E_2 + 8(3) = 0`
or `E_2 = 54V`
c. From loop (3),
`-2R -E_1 + E_2 = 0`
or `R = (E_2-E_1)/2 = -36 = 9W`.