Subjects electrical engineering

Kvl Equation 4621D8

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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.