Understanding Current in Series Circuits with Constant Voltage

This question explores a fundamental concept in electrical circuits, specifically how adding components in a series circuit affects the overall current when the voltage is kept constant. It relies on Ohm's Law, which describes the relationship between voltage, current, and resistance.

What Happens When Lamps are Added in Series?

In an electrical circuit, lamps act as resistors because they impede the flow of electric current. When multiple components, like lamps, are connected in series, their resistances add up.

• If you have one lamp with resistance $R_1$, the total resistance is $R_1$.
• If you add a second lamp with resistance $R_2$ in series, the total resistance becomes $R_{total} = R_1 + R_2$.
• If you add a third lamp with resistance $R_3$ in series, the total resistance becomes $R_{total} = R_1 + R_2 + R_3$.

So, adding more lamps in series increases the total resistance of the circuit.

Applying Ohm's Law

Ohm's Law states the relationship between Voltage (V), Current (I), and Resistance (R) as:

$$V = I \times R$$

This can be rearranged to find the current:

$$I = \frac{V}{R}$$

The question states that the voltage (V) is kept constant. We have established that adding more lamps in series increases the total resistance ($R_{total}$). Let's see how this affects the current (I) using Ohm's Law:

• When resistance (R) increases, and voltage (V) remains constant, the current (I) must decrease to maintain the equality $V = I \times R$.
• Think of it like pushing water through a pipe. Voltage is the pressure pushing the water, current is the flow rate, and resistance is how narrow or blocked the pipe is. If you add more blockages (increase resistance) but keep the pressure the same (constant voltage), less water will flow (current decreases).

Conclusion

Keeping the voltage constant, if more lamps are put into a series circuit, the total resistance of the circuit increases. According to Ohm's Law ($I = V/R$), if the voltage stays the same and the resistance increases, the current must decrease.

Revision Table: Series Circuit Basics

Additional Information: Comparing Series and Parallel Circuits

It's helpful to compare this behavior to a parallel circuit:

• Parallel Circuit: When components are added in parallel, the total resistance decreases. If voltage is kept constant, adding more components in parallel would increase the total current ($I = V/R_{total}$, if $R_{total}$ decreases, $I$ increases). This is why lights in a house are wired in parallel – if you add more lights, the total resistance decreases, and the total current drawn from the source increases, but each light gets the full voltage and operates independently.
• Series Circuit: As discussed, adding components in series increases total resistance, causing the total current to decrease at constant voltage. If one lamp in a series circuit burns out (becomes an open circuit), the entire circuit is broken, and no current flows, so all lamps go out.

Understanding the difference between series and parallel circuits is key to solving many electrical problems.