Each of the four circuits in the drawing consists of a...

Each of the four circuits in the drawing consists of a single resistor whose resistance is either $R$ or $2 R,$ and a single battery whose voltage is either $V$ or 2$V .$ The unit of voltage in each circuit is $V=12.0 \mathrm{V}$ and the unit of resistance is $R=6.00 \Omega$ . Determine $\quad$ (a) the power supplied to each resistor and $(\text { b) the current delivered to each }$ resistor.

Each of the four circuits in the drawing consists of a single resistor whose resistance is either $R$ or $2 R,$ and a single battery whose voltage is either $V$ or 2$V .$ The unit of voltage in each circuit is
$V=12.0 \mathrm{V}$ and the unit of resistance is $R=6.00 \Omega$ . Determine $\quad$ (a) the power supplied to each resistor and $(\text { b) the current delivered to each }$ resistor.

Key Concepts

Ohm's Law

Ohm's Law is a fundamental principle that expresses the relationship between voltage, current, and resistance in an electrical circuit through the equation V = IR. This concept is essential for determining how changes in voltage or resistance affect the current in the circuit.

Electrical Power

Electrical power is the rate at which energy is transferred or converted in an electrical circuit. It is commonly calculated using formulas such as P = IV, P = V²/R, or P = I²R, depending on the known variables. Understanding these relationships is key to evaluating energy consumption and heat generation in resistive elements.

Unit Analysis and Scaling

Unit analysis and scaling are important when dealing with standardized component values, such as a base voltage and resistance. This concept helps in understanding how multiplying the base values by certain factors (e.g., using 2V or 2R) affects the overall behavior of the circuit, particularly the resulting currents and power outputs.

Resistive Circuit Analysis

Resistive circuit analysis involves studying circuits that primarily contain resistors and power sources. This concept includes applying Ohm's Law and power formulas to determine the electrical characteristics, such as the current through and power dissipated by each resistor, given different combinations of voltages and resistances.

Transcript

00:01 In this problem, in each figure, the value of r is 6o, and the value of v is 12 volt.

00:10 Now, you can see that some of them are r, some of them are 2r for the resistance, and some of them are v, and some of them are 2v for their voltages.

00:19 So let's first find out in part a.

00:22 First find out the power delivered in each rate of resistance.

00:25 Okay, so let's begin.

00:28 Part a for figure a you can see that the power delivered pa is going to be equal to v a squared over r a which is also v squared over r which is 12 volt squared over 6 om which is is it going to be equal to 24 watt all right now for figure b figure b figure b you can see v equals vb equals vrr rb equals 2r so pb is going to be equal to this is figure b by the way pb is going to be equal to b b squared over rb and vb was v so v squared over rb equals 2r and this is going to be 12 volt squared over 12 o 'clock which is going to be equal to 12 watt.

01:46 Now for figure c power delivered is going to be equal to vc squared over rc and the vc squared is going to be 2 volt squared sorry 2 v squared over r c was r so 2 times 12 volt squared over 12 sorry 6 o this is 6 om.

02:25 And this is going to give us 12 times to 24 squared over 6 om, which is 96 watt.

02:34 Now for figure d, pd is going to be equal to vd squared over rd, which is 2v squared over 2r, 2r squared over 2r equals 24 volt.

02:58 2 times 12 volt over 12 om, 24 volt squared, square over 12 om, and this is going to give us 48 watt.

03:19 So one thing i want to mention here is this is not 2 volt...

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