Understanding the Changes in Voltmeter and Ammeter Readings When Connecting Resistors in Series vs Parallel

When resistors are connected in series or parallel, the readings of a voltmeter and ammeter can change significantly. This article will break down how these changes occur and provide a comprehensive overview of the readings for both configurations.

Resistors in Series

When resistors are connected in series, the total resistance (R_{text{total}}) is the sum of individual resistances. The formula for calculating R_{text{total}} is given by:

R_{text{total}} R_1 R_2 ldots R_n

The current (I) flowing through the circuit, as measured by the ammeter, can be calculated using Ohm's Law:

I frac{V}{R_{text{total}}}

where V is the voltage supplied by the source.

When a voltmeter is connected across each resistor, it measures the voltage drop (V_i) across that resistor, using the formula:

V_i I cdot R_i

The total voltage (V) across the series circuit is the sum of the voltage drops across each resistor:

V V_1 V_2 ldots V_n

Resistors in Parallel

When resistors are connected in parallel, the total resistance (R_{text{total}}) is given by the reciprocal of the sum of the reciprocals of the individual resistances. The formula is:

frac{1}{R_{text{total}}} frac{1}{R_1} frac{1}{R_2} ldots frac{1}{R_n}

The total current (I) supplied by the voltage source is now divided among the parallel branches. The current (I_i) through each resistor can be expressed as:

I_i frac{V}{R_i}

The total current (I) is the sum of the currents through each branch:

I I_1 I_2 ldots I_n

When a voltmeter is connected across the whole parallel circuit, it measures the total voltage (V) which is the same across all resistors. Thus each resistor experiences the same voltage V:

V V_1 V_2 ldots V_n

Summary of Changes

In Series

Ammeter Reading: The current is the same throughout the circuit and is less than if the resistors were not present. Voltmeter Reading: Measures the total voltage across the entire series circuit which is the sum of the individual voltage drops across each resistor.

In Parallel

Ammeter Reading: The total current is greater than when the resistors are in series as the total resistance is lower. Voltmeter Reading: Measures the same voltage across each resistor equal to the voltage of the source.

Conclusion

Switching from series to parallel typically increases the ammeter reading due to a decrease in total resistance, while the voltmeter reading across each resistor in parallel remains constant and equal to the source voltage.

For further learning, consider these related topics:

Understanding Electrical Circuits Applying Ohm's Law in Practical Scenarios Comparing Series and Parallel Circuits in Real-Life Applications