Coils Connected in Series

Definition

A series connection of coils is an arrangement in which coils are joined end to end so that the same current passes through all of them, and the total inductance, resistance, and impedance of the combination depend on the individual values and mutual interaction of the coils.

Main Content

1. Series Connection and Current Flow

• In a series arrangement, coils are connected one after the other, forming only one path for current.
• The same current flows through every coil because there is no branching in the circuit.

When coils are connected in series, the current entering the first coil is exactly the same as the current leaving the second, third, or any other coil in the series. This is one of the most important characteristics of a series circuit. Since the current remains identical in all coils, the magnetic effects produced by each coil depend on that common current. If the coils have different resistances or inductive reactances, the voltage drop across each coil may vary, but the current remains constant throughout the entire series path.

For example, if three coils are connected in series across an AC supply, the same alternating current passes through all three coils. If one coil has a higher inductive reactance, it will oppose the current more strongly and create a larger voltage drop across itself than the others. However, the current through all coils will still be the same because the circuit offers only one path.

2. Total Inductance of Coils in Series

• The total inductance of series-connected coils is generally the sum of individual inductances.
• If mutual coupling exists between coils, the total inductance may increase or decrease depending on the direction of flux linkage.

For uncoupled coils, the equivalent inductance of a series combination is simply:

$$L_{eq} = L_1 + L_2 + L_3 + \cdots$$

This means that connecting coils in series is a useful way to increase the total inductance of a circuit. However, in practical circuits, coils may be magnetically coupled. In that case, the magnetic field of one coil affects the other, and the total inductance depends on whether the mutual flux aids or opposes the individual fluxes.

If two coupled coils are connected in series:

Series aiding connection

• : the magnetic fields reinforce each other, so total inductance increases.

Series opposing connection

• : the magnetic fields oppose each other, so total inductance decreases.

For two coils with mutual inductance $M$:

• Series aiding:
  $$L_{eq} = L_1 + L_2 + 2M$$

• Series opposing:
  $$L_{eq} = L_1 + L_2 - 2M$$

This concept is very important in transformer windings, inductors, and magnetic circuits. For instance, if two identical coils of 5 H each are connected in series aiding and the mutual inductance is 1 H, the total inductance becomes 12 H, which is much larger than the simple sum without coupling considerations.

3. Voltage, Impedance, and Practical Behavior

• In series coils, the supply voltage is divided among the coils according to their impedance.
• The total impedance of the combination is the sum of individual impedances.

In AC circuits, coils do not behave like pure resistors. They offer inductive reactance in addition to resistance. Therefore, each coil has an impedance:

$$Z = R + jX_L$$

where $R$ is resistance and $X_L = 2\pi fL$ is inductive reactance.

For coils in series: $$Z_{total} = Z_1 + Z_2 + Z_3 + \cdots$$

This means the total impedance increases when more coils are added in series. As the impedance increases, the circuit current decreases for a given applied voltage. The voltage across each coil depends on its individual impedance. A coil with higher inductance or resistance will generally drop more voltage.

This principle is used in practical applications such as:

• limiting AC current,
• smoothing current in power supplies,
• tuning radio-frequency circuits,
• and designing filters.

For example, in a series combination of two coils, one with high inductance and another with lower inductance, the total impedance may become large enough to reduce current significantly. This is useful where current control is necessary without using resistors that waste more power as heat.

Working / Process

1. Two or more coils are connected end to end so that only one path is available for current flow.
2. When an electric supply is applied, the same current flows through every coil, and each coil develops its own voltage drop based on its impedance and inductive reactance.
3. The total effect of the combination is obtained by adding the individual inductances and impedances, while considering mutual coupling if the coils are magnetically linked.

Advantages / Applications

• It helps in increasing the total inductance of a circuit without using a single large coil.
• It is used in transformers, chokes, filters, and tuning circuits where controlled inductance is required.
• It is useful for current limiting, impedance matching, and magnetic field control in AC circuits.

Summary

• Coils connected in series carry the same current through all coils.
• The total inductance and impedance depend on the individual coils and their magnetic coupling.
• Series connection is widely used in practical electrical and electronic circuits for increasing inductance and controlling current.
• Important terms to remember: series connection, inductance, impedance, mutual inductance, series aiding, series opposing