The chain is composed, as shown in the figure, E ₁ = 1,8, E ₂ = 1,7, E B ₃ = 1,5, r ₁ = 0,2 Ohm, r ₂ = r ₃ = 0,1 Ohm.
Determine the resistance R and the current strength in all parts of the chain, if you know that the third element of the current is zero.
Цепь составлена, как показано на рисунке, Е₁=1,8В, Е₂=1,7В, Е₃=1,5В, r₁=0,2Ом, r₂=r₃=0,1Ом.
Определить сопротивление R и силу тока во всех участках цепи, если известно, что в третьем элементе сила тока равна нулю.
To determine the resistance R and the current strength in all parts of the chain, we need to apply the principles of circuit analysis. I will walk you through the steps:
1. Start by representing the given circuit elements and their values. In this case, we have three voltage sources E₁, E₂, and E₃, and three resistors r₁, r₂, and r₃. Also, we know that the current in the third element is zero.
2. Next, draw the circuit diagram. Based on the description, the circuit would consist of three resistors in series, with voltage sources connected in parallel to each resistor.
3. Use Kirchhoff's Voltage Law (KVL) to analyze the circuit. Apply KVL around the loop formed by the voltage sources and resistors connected in series. Since the third element's current is zero, we can ignore it in the analysis.
4. Write the KVL equation. Let's assume the total current in the circuit is I. The voltage drops across the resistors r₁, r₂, and r₃ can be calculated using Ohm's Law (V = I * R). The voltage drops across the voltage sources E₁, E₂, and E₃ can be written as E₁, E₂, and E₃, respectively. Therefore, the KVL equation becomes:
E₁ - I * r₁ - E₂ - I * r₂ - E₃ - I * r₃ = 0
5. Simplify the equation. Substitute the given values of E₁, E₂, E₃, r₁, r₂, and r₃ into the equation. Since the third element's current is zero, substitute I = 0 for the third element's current term. The equation will now contain only two unknowns, R (total resistance) and I (total current).
6. Solve the equation for R and I. Rearrange the equation to solve for R:
R = (E₁ - E₂ - E₃) / (I * (r₁ + r₂ + r₃))
7. Substitute the known values of E₁, E₂, E₃, r₁, r₂, and r₃ into the equation. Calculate the value of R.
8. Once you have the value of R, you can calculate the current in each part of the circuit. Since the resistors are connected in series, the total current I will pass through all three resistors. The current in each resistor can be calculated using Ohm's Law (I = V / R), where V is the voltage drop across the resistor.
Following these steps, you should be able to determine the resistance R and the current strength in all parts of the chain.