Voltage Division and Current Division in Electric Circuits

Voltage division and current division are important techniques used in electric circuit analysis. These methods help in determining voltage across resistors in series circuits and current through branches in parallel circuits.

---

Voltage Division in Series Circuit

In a voltage divider network, the voltage across each resistor in the series chain is directly proportional to the resistor value.

The current through all the resistances will be the same. A large resistance causes a large voltage drop, while a small resistance causes a small voltage drop.

For a series circuit containing resistors (R_1) and (R_2),

$$V = V_1 + V_2$$

Using Ohm’s law,

$$V_1 = IR_1$$ $$V_2 = IR_2$$

Since,

$$I = \frac{V}{R_1 + R_2}$$

Substituting for current,

$$V_1 = \frac{VR_1}{R_1 + R_2}$$

Similarly,

$$V_2 = \frac{VR_2}{R_1 + R_2}$$

Thus, the voltage across each resistor is proportional to its resistance.

---

Current Division in Parallel Circuit

Consider a two-branch parallel circuit as shown in Figure.

The branch currents (I_1) and (I_2) can be evaluated in terms of total current (I) as follows:

$$I_1 = I \frac{R_2}{R_1 + R_2}$$ $$I_2 = I \frac{R_1}{R_1 + R_2}$$

That is, current in one branch equals the total current multiplied by the resistance of the other branch and then divided by the sum of the resistances.

The branch having lower resistance carries higher current, while the branch having higher resistance carries lower current.

---

Summary

• Voltage division is applicable to series circuits.
• Current remains the same throughout a series circuit.
• Current division is applicable to parallel circuits.
• Voltage remains the same across all branches in a parallel circuit.
• Voltage and current division techniques simplify circuit analysis.