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<<< Kirchhoff's Questions Bank >>>

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\[1\star\]

In the circuit below, the current intensity \[ I_2 =?\]

\[i_2 =7 \;A\;\;\;\;\;\; -C \]

\[i_2 =15 \;A\;\;\;\;\;\; -A \]

\[i_2 = 3 \;A\ \;\;\;\;\;\; -D \]

\[i_2 =5 \;A \;\;\;\;\;\; -B \]

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    \[2\star\]

    In the loop marked with number 1
    The potential difference across the resistor \[ V_{R2} = ? \]

    \[ 𝑉_{𝑅2 }= 15.25 \;𝑉 \;\;\;\;\;\; -C \]

    \[𝑉_{𝑅2 }= 8.75 \;𝑉 \;\;\;\;\;\; -A \]

    \[𝑉_{𝑅2 }= 5.36 \;𝑉 \;\;\;\;\;\; -D \]

    \[𝑉_{𝑅2 }= 15.25 \;𝑉 \;\;\;\;\;\; -B \]

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    \[3\star\]

    In the figure below, the current passing through \[ R_1 , R_2 \] is equivalent to

    \[I_1 = 2\;A \;\;\;\;\;\;, \;\;\;\;\;\;I_2 =2 \;A -C \]

    \[I_1 = 1\;A \;\;\;\;\;\;, \;\;\;\;\;\;I_2 =4 \;A -A \]

    \[I_1 = 1\;A \;\;\;\;\;\;, \;\;\;\;\;\;I_2 =4 \;A -D \]

    \[I_1 = 1\;A \;\;\;\;\;\;, \;\;\;\;\;\;I_2 =1 \;A -B \]

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    \[4\star\]

    In the figure below, using Kirchhoff's laws, calculate the value of the unknown resistance \[ R= .... \]

    \[ R = 4\; Ω \;\;\;\;\;\; -C \]

    \[R = 2\; Ω \;\;\;\;\;\; -A \]

    \[R = 5\; Ω \;\;\;\;\;\; -D \]

    \[R =3\; Ω\;\;\;\;\;\; -B \]

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    \[5\star\]

    In the figure below, using Kirchhoff's laws, the value of the unknown resistance \[ R= .... \]
    equals

    \[ R = 15\; Ω \;\;\;\;\;\; -C \]

    \[R = 5\; Ω \;\;\;\;\;\; -A \]

    \[R = 20\; Ω \;\;\;\;\;\; -D \]

    \[R =10\; Ω\;\;\;\;\;\; -B \]

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    \[6\star\]

    In the figure below, using Kirchhoff's laws, the value of the unknown resistance \[ R= .... \] is equivalent to

    \[ R = 10\; Ω \;\;\;\;\;\; -C \]

    \[R = 8\; Ω \;\;\;\;\;\; -A \]

    \[R = 6\; Ω \;\;\;\;\;\; -D \]

    \[R =9\; Ω\;\;\;\;\;\; -B \]

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    \[7\star \star\]

    In the adjacent figure, the value of the variable resistance was changed until the galvanometer reading became zero. The value of the resistance \[ R_ X = .... \]

    \[ R = 5\; Ω \;\;\;\;\;\; -C \]

    \[R = 4\; Ω \;\;\;\;\;\; -A \]

    \[R = 3\; Ω \;\;\;\;\;\; -D \]

    \[R =6\; Ω\;\;\;\;\;\; -B \]

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    \[8\star \]

    The potential difference across the galvanometer equals zero
    when the resistance values equal

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    \[9\star \star\]

    An ammeter is used to measure current and is connected in series in the circuit. To increase the range of the ammeter for measurement, connect

    High resistance in parallel -C

    Small resistance in parallel -A

    High resistance in series -D

    Small resistance in series -B

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    \[10 \star\]

    A voltmeter is used to measure potential difference and is connected in parallel in the circuit. To increase the range of the voltmeter for measurement, connect

    High resistance in parallel -C

    Small resistance in parallel -A

    High resistance in series -D

    Small resistance in series -B

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    \[11 \star\]

    An ammeter is used to measure low currents. Its internal resistance is 2Ω. A learner wanted to double its ability to measure current by 50 times. The value of the resistance that needs to be connected in parallel to achieve the desired result equals

    \[ R = 0.04\; Ω \;\;\;\;\;\; -C \]

    \[R = 0.02\; Ω \;\;\;\;\;\; -A \]

    \[R = 0.05\; Ω \;\;\;\;\;\; -D \]

    \[R =0.03\; Ω\;\;\;\;\;\; -B \]

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    \[12 \star\]

    A voltmeter is used to measure a potential difference of 1v. Its internal resistance is 500Ω. A learner wanted to make the device capable of measuring a potential difference of 50v. The value of the resistance that needs to be connected in series to achieve the desired result equals

    \[ R = 37000 \; Ω \;\;\;\;\;\; -C \]

    \[R = 40000\; Ω \;\;\;\;\;\; -A \]

    \[R = 54000\; Ω \;\;\;\;\;\; -D \]

    \[R =24500 \; Ω\;\;\;\;\;\; -B \]

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    \[13 \star\]

    In the figure below at junction A, one of the following statements is correct

    \[𝐼_2+𝐼_3=𝐼_1 \;\;\;\;\;\; -C \]

    \[𝐼_2+𝐼_5+𝐼_4=𝐼_1 \;\;\;\;\;\; -A \]

    \[𝐼_3+𝐼_5+𝐼_4=𝐼_1 \;\;\;\;\;\; -D \]

    \[𝐼_2+𝐼_3+𝐼_5=𝐼_1 \;\;\;\;\;\; -B \]

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    \[14 \star\]

    In the circuit below, the battery voltage equals


    \[E=250 \;\;V\;\;\;\;\;\;-C\]

    \[E=300 \;\;V\;\;\;\;\;\;-A\]

    \[E=350 \;\;V\;\;\;\;\;\;-D\]

    \[E=150 \;\;V\;\;\;\;\;\;-B\]

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    \[15 \star\]

    In the figure below, the potential difference across the first and third resistors respectively equals

    \[V1=7\; V \;\;\;\;\;\; ,\;\;\;\;\;\; V3=5 \;V-C\]

    \[V1=7\; V \;\;\;\;\;\; ,\;\;\;\;\;\; V3=2 \;V-A\]

    \[V1=2\; V \;\;\;\;\;\; ,\;\;\;\;\;\; V3=7 \;V-D\]

    \[V1=5\; V \;\;\;\;\;\; ,\;\;\;\;\;\; V3=7 \;V-B\]

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    \[16\star \star\]

    In the figure below, the value of resistance \[R\] equals

    \[ R = 3.33\; Ω \;\;\;\;\;\; -C \]

    \[R = 6.42 \; Ω \;\;\;\;\;\; -A \]

    \[R = 5.35\; Ω \;\;\;\;\;\; -D \]

    \[R =2.5\; Ω\;\;\;\;\;\; -B \]

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    \[17\star \star \star\]

    In the figure below, the current passing through the \[1Ω\] resistor equals

    \[ 𝐼 =0.54 \;A \;\;\;\;\;\; -C \]

    \[ 𝐼 =0.54 \;A \;\;\;\;\;\; -A \]

    \[ 𝐼 =0.25 \;A \;\;\;\;\;\; -D \]

    \[ 𝐼 =0.35 \;A\;\;\;\;\;\; -B \]

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    \[18 \star\]

    An ammeter with internal resistance \[10 Ω\] can measure current up to \[8 mA\]. A student wanted to extend its range to measure current up to \[2A\] by connecting a parallel resistor. The required resistance value for this purpose is

    \[ R_s = 0.08 \; Ω \;\;\;\;\;\; -C \]

    \[R_s = 0.04 \; Ω \;\;\;\;\;\; -A \]

    \[R_s = 0.01\; Ω \;\;\;\;\;\; -D \]

    \[R_s =0.06\; Ω\;\;\;\;\;\; -B \]

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    \[19 \star \star \star\]

    A voltmeter has an internal resistance \[1000 Ω\] and can measure a potential difference of \[0.05 V\]. A student wanted to extend the device's range to measure a potential difference \[ 10 V\], so a series resistor was connected to increase the device's range. The required resistance value for this purpose equals

    \[ R_{es}=199000 \; Ω \;\;\;\;\;\; -C \]

    \[R_{es}=109000\; Ω \;\;\;\;\;\; -A \]

    \[R_{es} = 250000\; Ω \;\;\;\;\;\; -D \]

    \[R_{es} =165000\; Ω\;\;\;\;\;\; -B \]

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    \[20\star \star\]

    A capacitor with capacitance \[20𝜇𝐹\] uncharged was connected in series with a resistor \[150 Ω\] and a battery as shown in the figure below. The percentage of capacitor charge after a time of \[3 ms\] equals

    \[ 0.47 \;\;\;\;\;\;-C\]

    \[0. 75 \;\;\;\;\;\;-A\]

    \[ 0.82 \;\;\;\;\;\;-D\]

    \[0.63\;\;\;\;\;\;-B\]

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    \[21\star \star\]

    A capacitor with capacitance \[6𝜇𝐹 \] uncharged was connected in series with two resistors \[ R_1=90 Ω ,R_2=30 Ω \] and a battery with voltage \[50V\]. The time required to complete 50% charging of the capacitor equals

    \[t =4.45 ×10^{-5 } \;\;S\;\;\;\;\;\;-C\]

    \[t =9.35 ×10^{-5 } \;\;S\;\;\;\;\;\;-A\]

    \[t =2.18 ×10^{-5 } \;\;S\;\;\;\;\;\;-D\]

    \[t =6.86 ×10^{-5 } \;\;S\;\;\;\;\;\;-B\]

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    \[22 \star\]

    A capacitor with capacitance \[2𝜇𝐹\] was connected with two resistors \[ R_1=500 Ω ,R_2=300 Ω \] and a battery until the charging process was completed as shown in the figure below. The time constant for completing the discharging process equals

    \[𝜏=1.6×10^{-3} \;\;S\;\;\;\;\;\;-C\]

    \[𝜏=2.6×10^{-3} \;\;S\;\;\;\;\;\;-A\]

    \[𝜏=3.1×10^{-3} \;\;S\;\;\;\;\;\;-D\]

    \[𝜏=4.2×10^{-3} \;\;S\;\;\;\;\;\;-B\]

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    \[23 \star\]

    An electrical circuit consists of four resistors with values as shown in the figure below. The current intensity passing through each resistor is:

    \[I_1=0.35 A \;\;\;, \;\;\;I_2=0.35 A \;\;\;, \;\;\;I_3=0.7 A \;\;\;\;\;\;-C\]

    \[I_1=0.25 A \;\;\;, \;\;\;I_2=0.25 A \;\;\;, \;\;\;I_3=0.5 A \;\;\;\;\;\;-A\]

    \[I_1=0.2 A \;\;\;, \;\;\;I_2=0.2 A \;\;\;, \;\;\;I_3=0.4 A \;\;\;\;\;\;-D\]

    \[I_1=0.5 A \;\;\;, \;\;\;I_2=0.5 A \;\;\;, \;\;\;I_3=0.2 A \;\;\;\;\;\;-B\]

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    \[24 \star\]

    In the figure below, an electrical circuit is shown with resistors, batteries, current direction, and positive direction indicated. One of the equations correctly represents the equation of one of the loops in the circuit (Kirchhoff's second law):

    \[2−2I_1−2I_2−4I_3=0\;\;\;\;\;\;-C\]

    \[6−I_1−2I_2=0 \;\;\;\;\;\;-A\]

    \[4−I_1+4I_3=0\;\;\;\;\;\;-D\]

    \[2−2I_1−2I_2−4I_3=0\;\;\;\;\;\;-B\]

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    \[25 \star\]

    In the circuit below, the potential difference between points A and B equals:

    \[∆𝑉=11.44\;\;V \;\;\;\;\;\;-C\]

    \[∆𝑉=8.66\;\;V \;\;\;\;\;\;-A\]

    \[∆𝑉=5.42\;\;V \;\;\;\;\;\;-D\]

    \[∆𝑉=13.57\;\;V \;\;\;\;\;\;-B\]

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    \[26 \star\]

    A Wheatstone bridge was constructed using a copper wire of length 2m with a sliding contact point. Two resistors were placed on the other end: \[R_1=80 Ω , R_2=R\]. The contact point was moved until the galvanometer reading became zero at contact point C, which is 0.4 m from the end of the wire A. The value of \[R_2\] equals:

    \[ R_2 = 10\; Ω \;\;\;\;\;\; -C \]

    \[R_2 = 20\; Ω \;\;\;\;\;\; -A \]

    \[R _2= 30\; Ω \;\;\;\;\;\; -D \]

    \[R_2 =40\; Ω\;\;\;\;\;\; -B \]

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    \[27\star \star\]

    In the figure below, for loop 1 according to sign conventions and the assumed clockwise positive direction, one of the loop components has a negative voltage:

    21 ohm resistor -C

    5V battery -A

    7V battery-D

    10 ohm resistor-B

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    Solve the following problems

    \[1 \star \]

    In the figure below, an electrical circuit is shown. Calculate the current passing through the resistor \[R=6\;\;𝝮\]:

    \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] Calculate the power dissipated in the resistor \[R=2.5\;\;𝝮\]: \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\]
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  • \[2 \star \]

    An ammeter has an internal resistance of \[R_I= 27\;\;𝝮\] and can measure a current of \[I_I=0.1 \;\;A\]. A student wanted to increase the range of the device, so a resistance of \[R_S= 0.3\;\;𝝮\] was connected in parallel to measure a higher current. Calculate the current intensity increase factor: \[.........................................\;\;\;\;\;....................................\] \[.........................................\;\;\;\;\;....................................\] \[.........................................\;\;\;\;\;....................................\] \[.........................................\;\;\;\;\;....................................\]

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  • \[3 \star \]

    A capacitor with capacitance \[C= 20\;\;𝜇𝐹\] is uncharged and connected in series with a resistor \[R= 100\;\;𝝮\] and a battery with potential difference \[V= 20\;\;V\]:

    Calculate the time constant: \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] Calculate the time required until the current in the circuit becomes \[I= 0.1\;\;A\]: \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\]
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  • \[4 \star \]

    The circuit shown in the diagram contains two resistors and two capacitors connected to the battery via a switch. When the switch is closed, the capacitors begin to charge. Calculate the time constant for the charging process: \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\] \[.....................................\;\;\;\;............................................\]

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