1. **State the problem:** Write the Kirchhoff's Voltage Law (KVL) equation for the given circuit loop.
2. **Recall KVL:** The sum of all voltages around a closed loop equals zero.
3. **Identify voltages:** The loop has voltage sources $v_a$, $v_b$ and voltage drops across resistors $R_1$, $R_2$, $R_3$ with currents $i$.
4. **Write KVL equation:** Starting at the lower left corner and moving clockwise,
$$-v_a + v_1 + v_b + v_2 + v_3 = 0$$
5. **Express resistor voltages:** Using Ohm's law $v = iR$,
$$v_1 = i R_1, \quad v_2 = i R_2, \quad v_3 = i R_3$$
6. **Substitute into KVL:**
$$-v_a + i R_1 + v_b + i R_2 + i R_3 = 0$$
7. **Rearrange terms:**
$$v_b - v_a = i (R_1 + R_2 + R_3)$$
This is the KVL equation relating voltages and currents in the circuit loop.
Kvl Equation 4621D8
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