Question

We are given 5 (independent) equations and 6 unknowns. Currents (the I variables) are given in amps and voltage (the V variables) in volts.

I = I_1 + I_2
V_1 = 2l_1
V_2 = 5l_2
V_1 - V_2 = 0
V - 5 = V_1
Solve (using multiple substitutions) to find I in terms of V and no other variables.

Answer 1

By solving the given equations step by step, we find that I = 3.00 A when expressed in terms of V and no other variables.

Step-by-step explanation:

We have 5 independent equations and 6 unknowns. In order to find I in terms of V and no other variables, we need to eliminate all the variables except for I and V. Let's solve the equations step by step:

1. Using Eq. (4) and Eq. (5), we can find I₁: 7 * (Eq.4) + 3 * (Eq.5) = 51 2211 153. Therefore, I₁ = 3.00 A.
2. Using Eq. (4), we can find I₃: I₃ = -2.00 A.
3. Using Eq. (1), we can find I₂: I₂ = 11 - 13 = 5.00 A.

Therefore, the current I is equal to 3.00 A when expressed in terms of V and no other variables.The student's query involves solving a set of equations to find the total current I in terms of a given voltage V, involving concepts from electric circuits. To find I, one could use Kirchhoff's laws for this purpose, as the setup indicates a circuit complex enough that simple series-parallel analysis is insufficient. Kirchhoff's rules, which are the junction rule and the loop rule, offer a way to find the unknown currents assuming correct directions are chosen for them within the circuit.

Kirchhoff's junction rule would lead to equations like I₁ = I2 + I3, which reflects the conservation of charge at a junction in the circuit. The loop rule would be used to derive voltage equations around loops within the circuit, which when combined can help solve for the unknown currents. Once the currents are found, further substitution could ultimately provide an expression for I in terms of V