Practical Physics - Resistances in Series

Practical Physics: Resistances in Series

Experiment 4: Resistances in Series

Aims:

• To learn how to connect resistances in series in an electric circuit.
• To measure the resultant resistance of two resistances connected in series, both theoretically and experimentally.

Theory:

• Resistances in Series: When a number of resistances are connected in series, the current through each resistor is the same. However, the voltage across each resistor will be different.

• Current: In a series circuit, the current (I) is constant throughout:

  $I = I<em>1 = I</em>2 = I_3$

  where $I<em>1$, $I</em>2$, and $I_3$ are the currents through individual resistors.

• Voltage: The total voltage (V) across the series combination is the sum of the individual voltages:

  $V = V<em>1 + V</em>2 + V_3$

  where $V<em>1$, $V</em>2$, and $V_3$ are the voltages across individual resistors.

• Equivalent Resistance (Req): The equivalent resistance of a series combination can be derived as follows:

  $I R<em>{eq} = I R</em>1 + I R<em>2 + I R</em>3$
  $I R<em>{eq} = I (R</em>1 + R<em>2 + R</em>3)$
  $R<em>{eq} = R</em>1 + R<em>2 + R</em>3$

• For two resistors R1 and R2 connected in series, the equivalent resistance is:

  $R<em>{eq} = R</em>1 + R_2$

Equipment:

• Power supply
• Ammeter
• Wires
• Two resistors
• Multimeter
• Rheostat

Experimental Set-up and Procedures (Part 1: Measurement of Resistance in Series):

• a. Connect two resistors, $R<em>1$ and $R</em>2$, in series.
• b. Using the circuit, measure the current (I) and voltage (V).
• c. Repeat step 'b' six times and record the values in a table.
• d. Plot a graph of V (voltage) versus I (current). The slope of this graph is equal to the equivalent resistance, $R<em>{eq} = R</em>1 + R_2$.
• e. Compare the experimental value of $R_{eq}$ with the theoretical calculation of this value.
  • Note: Ideal values for $R<em>1$ and $R</em>2$ will be provided.
• f. Identify the possible sources of errors in the experiment.