Question

1. using the circuit drawings,

a) draw a voltmeter measuring the voltage for \\(r_2\\).
b) draw an ammeter measuring the current between the battery and \\(r_1\\) (before the junction/ split)
c) find the currents passing all the resistors
d) find the voltages for all the resistors.

Explanation:

Step1: Describe voltmeter connection

Connect the voltmeter in parallel across the terminals of resistor \(R_2\).

Step2: Describe ammeter connection

Connect the ammeter in series in the main wire before the junction.

Step3: Determine parallel voltages

Since the resistors are in parallel across a \(12\text{ V}\) source:

$$V_1 = V_2 = 12\text{ V}$$

Step4: Calculate current through \(R_1\)

Using Ohm's law with \(R_1 = 4\ \Omega\):

$$I_1 = \frac{V_1}{R_1} = \frac{12\text{ V}}{4\ \Omega} = 3\text{ A}$$

Step5: Calculate current through \(R_2\)

Using Ohm's law with \(R_2 = 6\ \Omega\):

$$I_2 = \frac{V_2}{R_2} = \frac{12\text{ V}}{6\ \Omega} = 2\text{ A}$$

Answer:

a) To measure the voltage across \(R_2\), connect a voltmeter in parallel with resistor \(R_2\).
b) To measure the total current before the split, connect an ammeter in series in the main branch between the battery and the junction leading to \(R_1\).
c) \(I_1 = 3\text{ A}\), \(I_2 = 2\text{ A}\) (assuming \(R_2 = 6\ \Omega\))
d) \(V_1 = 12\text{ V}\), \(V_2 = 12\text{ V}\)