Answer :
To find the value of the resistance [tex]R_3[/tex], we use Ohm's Law and the concept of series circuits.
Given:
- [tex]R_1 = 10.0 \, \Omega[/tex]
- [tex]V_b = 100 \, V[/tex]
- [tex]R_2 = 8.00 \, \Omega[/tex]
- Current [tex]I = 4.00 \, A[/tex]
In a series circuit, the total voltage [tex]V_t[/tex] is equal to the sum of the voltage drops across each resistor. The total resistance [tex]R_t[/tex] can be found using the formula:
[tex]R_t = R_1 + R_2 + R_3[/tex]
Ohm’s Law states:
[tex]V = IR[/tex]
For the entire circuit, the total voltage is the battery voltage [tex]V_b[/tex], and the current is [tex]I[/tex].
[tex]V_b = I \times R_t[/tex]
[tex]100 = 4 \times (10 + 8 + R_3)[/tex]
Solving for [tex]R_3[/tex]:
[tex]100 = 4 \times (18 + R_3)[/tex]
[tex]100 = 72 + 4R_3[/tex]
[tex]28 = 4R_3[/tex]
[tex]R_3 = \frac{28}{4}[/tex]
[tex]R_3 = 7 \, \Omega[/tex]
Therefore, the value of the resistance [tex]R_3[/tex] is [tex]7 \, \Omega[/tex].
The correct answer is C. 7 Ω.
