Answered

36 V
Three resistors: R₁-30, R2-6 Q, and R3-90 are connected in series to each other and to a 36 V battery. What is the ammeter reading after the
switch
is closed?
a) list all givens (0.6 Points)
b) list the unknown (0.6 Points)
c) show the formula (0.6 Points)
d) substitute the givens and solve the equation (0.6 Points)
e) list the answer with correct units

Verified Answer :

GinnyAnswer

Let's solve the problem step-by-step:

### a) List all givens
- Voltage (V) across the series circuit: 36 V
- Resistance of resistor 1: R₁ = 30 Ω
- Resistance of resistor 2: R₂ = 6 Ω
- Resistance of resistor 3: R₃ = 90 Ω

### b) List the unknown
The unknown is the current (I) flowing through the circuit.

### c) Show the formula
Ohm’s Law is used to relate voltage (V), current (I), and resistance (R). The formula is:
\(\[ V = I \times R \]\)

In a series circuit, the total resistance \(\( R_{\text{total}} \)\) is the sum of the individual resistances:
\(\[ R_{\text{total}} = R₁ + R₂ + R₃ \]\)

To find the current (I), rearrange Ohm's Law to:
\(\[ I = \frac{V}{R_{\text{total}}} \]\)

### d) Substitute the givens and solve the equation
1. Calculate the total resistance:
\(\[ R_{\text{total}} = R₁ + R₂ + R₃ \]\)
\(\[ R_{\text{total}} = 30 Ω + 6 Ω + 90 Ω \]\)
\(\[ R_{\text{total}} = 126 Ω \]\)

2. Calculate the current using Ohm's Law:
\(\[ I = \frac{V}{R_{\text{total}}} \]\)
\(\[ I = \frac{36 \text{ V}}{126 \text{ Ω}} \]\)
\(\[ I = 0.286 \text{ A} \]\)

### e) List the answer with correct units
The current flowing through the series circuit is 0.286 A (amperes).

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