Question

For the circuit shown below, determine the effective resistance of the entire circuit. Find the current flowing through and voltage drop across each resistor and draw the power box. If a compass was placed at points A, B and C, where would it point? Explain. SHOW ALL YOUR WORK PLEASE THANK YOU :)

12Ω 12Ω 15Ω 12Ω 12Ω 5.0 Ω

PLEASE EXPLAIN AND SHOW YOUR WORK PLEASE :)!!! THANK YOU SO MUCH

Answer 1

starting from upper right, 12 and 15 ohm are in parallel

so, their combined resistance is

R = 6.67 ohms

then at the bottom 12 and 12 ohms are parallel

their combined resistance is

R = 6 ohms

these above two are in series

so, we have 6 + 6.67 = 12.67 ohms

This is again in series with 12 ohms on the left and 5 ohms at the bottom

so finally

R (equivalent) = 29.67 ohms

Therefore,

I (equivalent) = V / R (equivalent) = 0.8426 A

Now,

the 12 ohm and 12.67 ohm and 5 ohm will have same current

then we need to open up 12.67 ohms

That means current in combination of (12 and 15) and (12 and 12) is same as 0.8426 A

Now,

voltage across these will be different as they are in series

V = 0.8426 * 6 = 5.055 V ( across 12 and 12 ohms)

V = 1.0134 * 6.67 = 5.62 V (across 12 and 15 ohms)

so,

current through 12 ohms = 0.42125 A ( In both 12 ohms at the bottom part)

current though 15 ohms = 0.3746 A

current through 12 ohms = 0.4683 A (This is the 12 ohms which was in parallel with 15 ohms - DO NOT GET CONFUSED)

Here is a brief picture with all the currents and voltages

12Ω l0.8426A 15 Ω l=0.3746 A I = 0.4683 V = 5.62 V V = 5.62 V 12 Ωに0.42125 A> 12 Ω l = 0.42125 A V=5.055 V V 5.055 V 1:0.8426 A 5.0 Ω V = 4.213 V

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Deflection of needle of compass can be determined using thumb rule.

As current is going from west to south in wire near point A, then deflection is towards north

At B, deflection is towards south