If a 10 $\mathrm { k } \Omega$ and 5 $\mathrm { k } \Omega$ resistor are connected in series across a 12V source, the voltage across the 10 k$\Omega$ resistor is and the voltage across the 5 $\mathrm { k } Q$ resistor is
A) 4 V, 8 V
B) 4 V, 4 V
C) 8 V, 4 V
D) 8 V, 8 V

Question

If a 10 $\mathrm { k } \Omega$ and 5 $\mathrm { k } \Omega$ resistor are connected in series across a  12V  source, the voltage across the  10 k$\Omega$ resistor is and the voltage across the 5 $\mathrm { k } Q$ resistor is
A)  4 V, 8 V
B)  4 V, 4 V
C)  8 V, 4 V
D)  8 V, 8 V

Quizplus · Accepted Answer

When two resistors are connected in series, the same current flows through both resistors. Using Ohm's law (V=IR), we can calculate the voltage drop (V) across each resistor.

First, we can calculate the total resistance (R) of the circuit by adding the resistances of the two resistors in series:
R = R1 + R2 = 10kΩ + 5kΩ = 15kΩ

Next, we can use Ohm's law to calculate the current (I) in the circuit:
I = V/R = 12V/15kΩ = 0.8mA

Finally, we can use Ohm's law again to calculate the voltage drop (V) across each resistor:
V1 = IR1 = (0.8mA)(10kΩ) = 8V
V2 = IR2 = (0.8mA)(5kΩ) = 4V

Therefore, the voltage across the 10 kΩ resistor is 8 V and the voltage across the 5 kΩ resistor is 4 V. The best choice is C, as it correctly identifies these values.

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