Correct answer: C — E = I × R (voltage equals current times resistance)

Ohm's Law states that the voltage (E) across a resistor equals the current (I) flowing through it multiplied by its resistance (R). This is one of the most fundamental relationships in electronics and applies to any purely resistive component.

\[ E = I \times R \]

Worked example: If 2 A flows through a 10 Ω resistor:

\[ E = 2 \times 10 = 20\ \mathrm{V} \]

• A. E = I + R — Incorrect; you cannot add current (amperes) and resistance (ohms) — they are different physical quantities with different units.
• B. E = I − R — Incorrect; subtraction of current and resistance is equally meaningless dimensionally.
• D. E = I / R — Incorrect; dividing current by resistance gives the wrong relationship. This formula is actually the rearrangement used to find current: I = E / R, not voltage.

Therefore, Ohm's Law E = I × R is the correct formula for calculating the voltage across a resistor carrying a known current through a known resistance.

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Correct answer: A — 5 volt

Ohm's Law states that the voltage across a resistor equals the current through it multiplied by its resistance.

\[ V = I \times R \]

Given:

• Current: 10 mA = 0.010 A
• Resistance: 500 Ω

\[ V = 0.010 \times 500 = 5\ \mathrm{V} \]

• B. 50 volt — Results from forgetting to convert milliamps to amps (using 0.1 A instead of 0.010 A).
• C. 500 volt — Confuses the resistance value with the voltage, or uses 1 A instead of 0.010 A.
• D. 5000 volt — Results from multiplying 10 (instead of 0.010) by 500, failing to convert mA to A.

Therefore, correctly applying Ohm's Law with the current converted to amps gives a voltage of 5 V across the 500 Ω resistor.

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Correct answer: 125 kilohm

Using Ohm’s Law:

\[ R = \frac{V}{I} \]

Given:

• \(V = 100\ \mathrm{V}\)
• \(I = 0.8\ \mathrm{mA} = 0.0008\ \mathrm{A}\)

Substituting:

\[ R = \frac{100}{0.0008} = 125{,}000\ \Omega = 125\ \mathrm{k}\Omega \]

• 125 \(\Omega\) would allow far too much current to flow.
• 1250 \(\Omega\) would also result in excessive current.
• 1.25 \(\mathrm{k}\Omega\) is incorrect by a factor of 100.

Therefore, the required resistance is 125 kilohm.

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Correct answer: A — Ohm's Law

Ohm's Law states that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance. The equation I = E/R is the standard expression of this relationship.

\[ I = \frac{E}{R} \]

Where:

• I = current in amperes (A)
• E = voltage (electromotive force) in volts (V)
• R = resistance in ohms (Ω)

For example, if 12 V is applied across a 4 Ω resistor:

\[ I = \frac{12}{4} = 3\ \mathrm{A} \]

• Thevenin's Theorem is a circuit simplification technique that replaces a complex network with an equivalent voltage source and series resistance — not described by I = E/R directly.
• Kirchhoff's First Law (the Current Law) states that the sum of currents entering a junction equals the sum leaving it — a topology rule, not this equation.
• Kirchhoff's Second Law (the Voltage Law) states that the sum of voltages around any closed loop equals zero — again a circuit topology rule, not this equation.

Therefore, I = E/R is the classic mathematical statement of Ohm's Law, one of the most fundamental relationships in electronics.

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Correct answer: B — 220 volt

Ohm's Law states that voltage equals current multiplied by resistance. With a current of 4.4 A flowing through a 50 Ω resistor, the required voltage is found directly from this relationship.

\[ V = I \times R \]

Given:

• I = 4.4 A
• R = 50 Ω

\[ V = 4.4 \times 50 = 220\ \mathrm{V} \]

• A — 2220 volt: This is approximately ten times too large; a likely result of a decimal point error or multiplying 4.4 × 500.
• C — 22.0 volt: This is ten times too small; equivalent to using 4.4 × 5 instead of 4.4 × 50.
• D — 0.222 volt: This results from dividing current by resistance (4.4 ÷ 50 × some factor) rather than multiplying — an inversion of Ohm's Law.

Therefore, applying Ohm's Law (V = IR) with 4.4 A and 50 Ω gives exactly 220 V.

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Correct answer: D — 32 volt

Ohm's Law states that voltage equals current multiplied by resistance. With 2 amperes flowing through 16 ohms, the applied voltage is found directly by substitution.

\[ V = I \times R \]

Given:

• Current I = 2 A
• Resistance R = 16 Ω

\[ V = 2 \times 16 = 32\ \mathrm{V} \]

• A — 8 volt: This is the result of dividing 16 by 2 (R ÷ I), which inverts the correct relationship.
• B — 14 volt: This is simply 16 − 2, an arithmetic error with no basis in Ohm's Law.
• C — 18 volt: This is 16 + 2, again an arithmetic error unrelated to the correct formula.

Therefore, applying Ohm's Law (V = IR) gives an applied voltage of 32 volts.

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Correct answer: D — 250 volt

Ohm's Law states that the voltage across a resistance equals the current through it multiplied by the resistance value.

\[ V = I \times R \]

Given:

• Current I = 5 A
• Resistance R = 50 Ω

\[ V = 5 \times 50 = 250\ \mathrm{V} \]

• A. 20 volt — This would result from dividing the resistance by the current (50 ÷ 5 = 10… not even 20), not applying Ohm's Law correctly.
• B. 45 volt — This is simply 50 − 5 = 45, incorrectly subtracting the values rather than multiplying.
• C. 55 volt — This is simply 50 + 5 = 55, incorrectly adding the values rather than multiplying.

Therefore, applying Ohm's Law (V = IR), a current of 5 A through a 50 Ω resistance produces a potential difference of 250 V.

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Correct answer: A — 5 volt

Ohm's Law states that voltage equals current multiplied by resistance. Given a current of 200 mA and a resistance of 25 Ω, the required voltage is calculated directly.

\[ V = I \times R \]

Given:

• I = 200 mA = 0.2 A
• R = 25 Ω

\[ V = 0.2 \times 25 = 5\ \mathrm{V} \]

• 8 volt — This does not result from any standard application of Ohm's Law with these values.
• 175 volt — This appears to come from subtracting 25 from 200 (treating mA as A), which is incorrect.
• 225 volt — This appears to come from adding 25 to 200 (treating mA as A), which is also incorrect and ignores the milliamp conversion.

Therefore, applying Ohm's Law correctly with the current converted to amps gives a supply voltage of 5 V.

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Correct answer: reduced to 3 volt

Using Ohm’s Law:

\[ R = \frac{V}{I} = \frac{6}{0.5} = 12\ \Omega \]

To get a current of 0.25 A through the same resistance:

\[ V = IR = 0.25 \times 12 = 3\ \mathrm{V} \]

• 12 V would increase current.
• Holding constant would keep current the same.
• Zero volts gives zero current.

Therefore, the voltage must be reduced to 3 volt.

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Correct answer: B — I = E / R [current equals voltage divided by resistance]

Ohm's Law states that the current flowing through a resistor is equal to the voltage across it divided by its resistance. This is one of the most fundamental relationships in electronics.

\[ I = \frac{E}{R} \]

Where:

• I = current in amperes (A)
• E = voltage (electromotive force) in volts (V)
• R = resistance in ohms (Ω)

Worked example: If 12 V is applied across a 4 Ω resistor:

\[ I = \frac{12}{4} = 3\ \mathrm{A} \]

• A: I = E × R — Multiplying voltage by resistance gives units of V·Ω, which is not current. This would actually be the formula for voltage (E = I × R) rearranged incorrectly.
• C: I = E + R — Adding voltage and resistance is dimensionally meaningless; you cannot add volts to ohms.
• D: I = E − R — Subtracting resistance from voltage is equally meaningless dimensionally and has no basis in circuit theory.

Therefore, Ohm's Law expressed as I = E / R is the correct formula for calculating current through a resistor.

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Correct answer: A — 12 / 8 amps

Ohm's Law states that current equals voltage divided by resistance. With 12 V across an 8 Ω resistor, the current is found by dividing the voltage by the resistance.

\[ I = \frac{V}{R} \]

Given:

• V = 12 V
• R = 8 Ω

\[ I = \frac{12}{8} = 1.5\ \mathrm{A} \]

• B. 8 / 12 amps — This inverts the formula (R ÷ V), which has no physical meaning in this context.
• C. 12 − 8 amps — Subtraction has no role in Ohm's Law; this confuses the relationship between voltage, current, and resistance.
• D. 12 + 8 amps — Addition is equally incorrect; voltage and resistance are not added to find current.

Therefore, applying Ohm's Law (I = V / R) gives a current of 12 / 8 = 1.5 A.

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Correct answer: 500 mA

Using Ohm’s Law:

\[ I = \frac{V}{R} \]

Given:

• \(V = 50\ \mathrm{V}\)
• \(R = 100\ \Omega\)

Substituting:

\[ I = \frac{50}{100} = 0.5\ \mathrm{A} = 500\ \mathrm{mA} \]

• 50 mA would require a much higher resistance.
• 2 A would require a resistance of only \(25\ \Omega\).
• 20 A would require a resistance of \(2.5\ \Omega\).

Therefore, the current flow is 500 mA.

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Correct answer: R = E / I

This is Ohm’s Law, which relates voltage (\(E\)), current (\(I\)), and resistance (\(R\)):

\[ R = \frac{E}{I} \]

• \(R = I / E\) is incorrect.
• \(R = E \times I\) gives power, not resistance.
• \(R = E / R\) is not valid.

Therefore, resistance is given by R = E / I.

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Correct answer: 10 kilohm

Ohm’s law relates voltage, current, and resistance:

\[ R = \frac{V}{I} \]

Given:

• \(V = 10\ \mathrm{V}\)
• \(I = 1\ \mathrm{mA} = 0.001\ \mathrm{A}\)

Substituting:

\[ R = \frac{10}{0.001} = 10{,}000\ \Omega = 10\ \mathrm{k}\Omega \]

• 10 ohm would require a current of \(1\ \mathrm{A}\) at 10 V.
• 100 ohm would require a current of \(0.1\ \mathrm{A}\) at 10 V.
• 1 kilohm would require a current of \(10\ \mathrm{mA}\) at 10 V.

Therefore, a resistor with 10 V applied and 1 mA flowing has a value of 10 kilohm.

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Correct answer: A — 10 ohm

Ohm's Law states that resistance equals voltage divided by current. With 3 V driving 300 mA (0.3 A) through a circuit, the resistance works out to exactly 10 ohms.

\[ R = \frac{V}{I} \]

Given:

• V = 3 V
• I = 300 mA = 0.3 A

\[ R = \frac{3}{0.3} = 10\ \Omega \]

• 9 ohm — incorrect; no combination of the given values produces this result.
• 5 ohm — incorrect; this would require 0.6 A at 3 V, not 0.3 A.
• 3 ohm — incorrect; this would require 1 A at 3 V, not 0.3 A.

Therefore, applying Ohm's Law directly gives a circuit resistance of 10 ohms.

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Correct answer: 24 ohms

Using Ohm’s Law:

\[ R = \frac{V}{I} \]

Given:

• \(V = 12\ \mathrm{V}\)
• \(I = 0.5\ \mathrm{A}\)

Substituting:

\[ R = \frac{12}{0.5} = 24\ \Omega \]

• 6 \(\Omega\) would result in a much higher current.
• 12.5 \(\Omega\) and 17 \(\Omega\) do not satisfy the given voltage and current.

Therefore, the value of the resistor is 24 ohms.

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Correct answer: D — 0.5 megohm

Resistance is measured in ohms (Ω). The greater the resistance value, the greater the opposition to current flow (by Ohm's Law: I = V/R — a larger R means less current for the same voltage). Comparing all options requires converting each to the same unit:

• 230 ohm = 230 Ω
• 1.2 kilohm = 1,200 Ω
• 1600 ohm = 1,600 Ω
• 0.5 megohm = 500,000 Ω

0.5 megohm is by far the largest value.

• 230 ohm — only 230 Ω, the smallest value listed and therefore the least opposition to current flow.
• 1.2 kilohm — 1,200 Ω, larger than 230 Ω but far smaller than 0.5 MΩ.
• 1600 ohm — 1,600 Ω, the second largest, but still only about 0.3% of 0.5 MΩ.

Therefore, 0.5 megohm (500,000 Ω) provides the greatest opposition to current flow of the four options given.

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Correct answer: D — electrical resistance

The ohm (Ω) is the SI unit of electrical resistance. Resistance is the property of a material or component that opposes the flow of electric current. A resistance of one ohm allows one ampere of current to flow when one volt is applied across it, as expressed by Ohm's Law:

\[ R = \frac{V}{I} \]

• A. supply voltage — Voltage (electrical pressure) is measured in volts, not ohms.
• B. electrical pressure — "Electrical pressure" is an informal term for voltage, which is measured in volts (V).
• C. current flow — Current is measured in amperes (A), not ohms.

Therefore, the ohm is the unit of electrical resistance, quantifying how strongly a component opposes the passage of current.

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Correct answer: D — 80 ohm

Ohm's Law states that resistance equals voltage divided by current. Given a 12 V supply and a current of 0.15 A, the resistance can be calculated directly.

\[ R = \frac{V}{I} \]

Substituting the values:

\[ R = \frac{12}{0.15} = 80\ \mathrm{\Omega} \]

• A — 0.15 ohm: This is simply restating the current value in ohms, not applying Ohm's Law at all.
• B — 1.8 ohm: This is the result of multiplying V × I (12 × 0.15 = 1.8), which gives power in watts, not resistance.
• C — 12 ohm: This is the supply voltage value, not the result of dividing voltage by current.

Therefore, applying Ohm's Law (R = V ÷ I) gives a circuit resistance of 80 ohms.

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Correct answer: 2.5 mA

Using Ohm’s Law:

\[ I = \frac{V}{R} \]

Given:

• \(V = 12\ \mathrm{V}\)
• \(R = 4800\ \Omega\)

Substituting:

\[ I = \frac{12}{4800} = 0.0025\ \mathrm{A} = 2.5\ \mathrm{mA} \]

• 25 mA would require a lower resistance.
• 40 A and 400 A are far too large for this resistance.

Therefore, the current flow is 2.5 mA.

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