Each month, College of Science alumni have the opportunity to test their skills and solve a current science student exam w88 slot online. These questions are posed in the monthly College of Science newsletter,Discovery Monthly. The very first Science w88 slot online of the Month was featured in the 2022 alumni magazineDiscovery.
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The January Science w88 slot online of the Month, provided by physics professor Kristin Lewis, was pulled from a Physics 181 exam.
w88 slot online
Calculate the current.
Consider the direct current (DC) w88 slot online pictured, which contains one battery of terminal voltage DV = 11 Volts [V], and three different resistors, each with resistance measured in Ohms [W] and proportional to resistance R.
The w88 slot online starts at the positive terminal of a battery labeled "delta V", extends up to a resistor labeled 3R, and extends to the right to split into two parallel vertical branches. The branch on the left has a resistor labeled R. The branch on the right has a resistor labeled 2R . The branches recombine, and the w88 slot online ends at the negative terminal of the battery.
What is w88 slot online the resistor of resistance R? Your answer should be in units of Amperes [A], and it will be a function of R.
Solution
Note the following relationship between units: [1 Ampere] = [1 Volt]/[1 Ohm]. Units have been suppressed in the solution.
Step 1: Find the equivalent resistance of the combination of resistors. First, combine the two resistors in parallel: 2R and R. Label the equivalent resistance of this combination as RR2R, and sketch the “intermediate” w88 slot online.
(1/R)+(1/2R)=(1/RR2R)
Therefore,
RR2R=(2R/3)
Next, combine the two remaining resistors, which are in series. Label the equivalent resistance, which is the equivalent resistance of the entire w88 slot online, Req.
Req=3R+RR2R=3R+(2R/3)=(11R/3)
Step 2: Find the current drawn from the battery. The potential difference across Req is equal to the potential difference across the terminals of the battery, and the potential difference across any resistor is equal to w88 slot online it times its resistance (▲V=IR, *important relationship*). Therefore, the current drawn from the battery of terminal voltage 11 V is
I=(▲V/Req)=(11/[11R/3])=(3/R)
Step 3: Consider this current, I, through the “intermediate circuit”. Because the two resistors are in series w88 slot online each is the same and equal to I=(3/R). Solve for the potential difference across RR2R:
(Check: ▲V3R=I(3R)=(3/R)(3R)=9, ▲V3R+▲VR2R=9+2=11=▲V)
▲VR2R=I(RR2R)=(3/R)(2R/3)=2
Step 4: Consider the original w88 slot online. The potential difference across resistors in parallel is the same. Therefore, the potential difference across resistors R and 2R is equal to that across their equivalent resistor RR2R: ▲VR=▲V2R=▲VR2R=2. Knowing the potential difference across R, solve for w88 slot online it, IR:
IR = (/R)=(2/R)
(Check: I2R=[▲V2R/2R]=[2/2R]=[1/R], IR+I2R=[2/R]+[1/R]=[3/R]=I)
Answer:
IR = 2/R (units: A)
January's Winner
January's winner was Gunes w88 slot online, who was first to submit the correct response. Congratulations, Gunes w88 slot online!
w88 slot online graduated from the University of Nevada, Reno with her master's degree (2005) and doctoral degree (2017) in physics. w88 slot online grew up in Turkiye (formerly known as Turkey). She has been working for the State Department of Education in Carson City since 2013. She is shown here with her miniature Australian Shepherd, Prince. Earthquake in Turkey and Syria: a reminder that when tragedy occurs w88 live casino, the world
