To find the resistance of component
b, we need to understand how parallel circuits work.
Step 1: Understand the Voltage
In a parallel circuit, the voltage across each branch is the same as the voltage of the battery.
* Battery Voltage = $4.5\text{ V}$
* Therefore, the voltage across resistor
a is $4.5\text{ V}$.
* The voltage across component
b is also $4.5\text{ V}$.
Step 2: Calculate the Current in Branch 'a'
We know the resistance of branch
a ($10\ \Omega$) and the voltage across it ($4.5\text{ V}$). We can use Ohm's Law ($I = V / R$) to find the current flowing through it.
* Current in
a ($I_a$) = $4.5\text{ V} / 10\ \Omega$
* $I_a = 0.45\text{ A}$
Step 3: Calculate the Resistance of Component 'b'
Now look at branch
b. We know two things about it:
1. The voltage across it is $4.5\text{ V}$ (from Step 1).
2. The current flowing through it is given in the diagram as $0.9\text{ A}$.
We can use Ohm's Law again to find the resistance ($R = V / I$):
* Resistance of
b ($R_b$) = Voltage / Current
* $R_b = 4.5\text{ V} / 0.9\text{ A}$
* $R_b = 5\ \Omega$
Final Answer:
The resistance of component b is 5 Ω.
Parent Tip: Review the logic above to help your child master the concept of electric circuits worksheet with answers.
