Question

Draw a circuit diagram showing the above two resistors X and Y joined in parallel with the same battery and same ammeter and voltmeter.

Answer 1

Parallel Resistor Circuit Overview

Two resistors, where \[ R_X = 3\,\Omega \] and \[ R_Y = 6\,\Omega \], are connected in parallel to a \[ 2\,\text{V battery} \]. An ammeter measures the total current, and a voltmeter is placed across the parallel combination.

Circuit Diagram (ASCII)

      + 2V -         ┌────┬────────────┬───────┐         │    │            │       │         │   [3Ω]         [6Ω]     │         │    │            │       │        (V)  └────┬────────┘       │                 │                │                (A)              GND  

Key Points:

• Resistors X (3 Ω) and Y (6 Ω) are in parallel.
• The voltage across both resistors is \[ V = 2\,\text{V} \].
• Individual resistor currents:
  • \( I_X = \frac{V}{R_X} = \frac{2}{3} \, \text{A} \)
  • \( I_Y = \frac{V}{R_Y} = \frac{2}{6}\)

Answer 2

Parallel Combination:
- Potential Difference (X and Y): In a parallel circuit, the potential difference across resistors X and Y is identical, as both are linked to the same battery. Thus, the potential difference across X and Y is equal in a parallel setup. - Current (X and Y): In a parallel circuit, the total current from the battery splits between the resistors. The current through each resistor is not necessarily the same, unless their resistances are equal. Series Combination:
- Identical current flows through X and Y since they are connected in series.
- The potential difference across each resistor differs, due to differing resistances.

Answer 3

To determine the current from the battery in a series circuit, calculate the total resistance. \[R_{\text{total}} = R_X + R_Y = 3 \, \Omega + 6 \, \Omega = 9 \, \Omega\] Next, apply Ohm's law to find the current: \[I = \frac{V}{R_{\text{total}}} = \frac{2 \, \text{V}}{9 \, \Omega} = 0.222 \, \text{A}\] The series combination draws 0.222 A from the battery.

Answer 4

To find the equivalent resistance of parallel resistors X and Y, we use the parallel resistor formula: \[\frac{1}{R_{\text{eq}}} = \frac{1}{R_X} + \frac{1}{R_Y}\] Substituting the values: \[\frac{1}{R_{\text{eq}}} = \frac{1}{3 \, \Omega} + \frac{1}{6 \, \Omega} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}\] Therefore, the equivalent resistance is: \[R_{\text{eq}} = 2 \, \Omega\]