a.
The equivalent resistance of a series combination of two resistors is equal to the sum of the individual resistances:
In this circuit, we have
Therefore, the equivalent resistance is
b. 5.8 V, 3.2 V
First of all, we need to determine the current flowing through each resistor, which is given by Ohm's law:
where V = 9.00 V and . Substituting,
Now we can calculate the potential difference across each resistor by using Ohm's law again:
Answer:
Part A: The voltage across resistor R1 is approximately .
Part B: When the value of resistor R1 decreases, the current in this circuit will increase.
Part C: When the value of resistor R1 decreases, the voltage across resistor R1 will decrease.
Explanation:
<h3>Part A</h3>Resistor R1 and and R2 are connected in series. That's equivalent to a single resistor of . The voltage across the two resistor, combined, is equal to
. Hence by Ohm's Law, the current through the circuit will be equal to
.
These two resistors are connected in series. The voltage across each of them might differ. However, the current through each of them should both be equal to the current through the circuit. In this case, the current through both R1 and R2 should be equal to . Apply Ohm's Law (again) to find the voltage across R1:
.
Since the equivalent resistance is equal to , when the value of
decreases, the equivalent resistance will also decrease. By Ohm's Law,
. When the value of the denominator ( decreases, the value of the quotient,
the current through the circuit, will increase.
Keep in mind that if two resistors are connected in series,
.
The resistance of R1 decreases, while the current through it increases. Applying Ohm's Law on R1 won't give much useful information. However, since the resistance of R2 stays the same, the voltage across it will increase when its current increases (again by Ohm's Law.)
Again, since the two resistors are connected in series,
,
when the voltage across R2 increases, the voltage across R1 will decrease.