PHYS 241-1 Test 3 Key 10/18/18 p. 1
1. a. Use Kirchhoff’s loop rule. For loop 1 start at the positive terminal of the 6.00 v battery and proceed
clockwise around the loop. For loop 2 start at the positive terminal of the 12.0 v battery and proceed
counterclockwise around the loop. (There are other correct ways to write the loop rule for these loops.)
1 1 2 1 1 1 2
2 1 2 2 1 2
11
Loop 1: 4 10 10 5 6 2 0 21 10 6
Loop 2: 10 10 12 2 0 10 13 12
Using Cramer's rule:
21 10 ; 21 13 10 10; 173
10 13
6 10
1 6 13 10 12
;
12 13
173 1
I I I I I or I I
I I I I or I I
II
1
2 2 2
; 0.243 A (10 points)
73
21 6
1 21 12 6 10
; ; 1.11 A (10 points)
10 12
173 173
I
I I I
b. Let point a be the ground below resistor R3 and point b be the junction above resistor R3. The electric
potential at point b is
a 1 2 b 1
a b 1
b
+10 10 Note that we treat as if its direction is correct.
Since 0 10 0.243 10 1.11 The negative value of makes the direction correction for us.
So 8.67 V . (15 points)
V I I V I
V V I
V
c. Since a fully-charged capacitor behaves is an open circuit, the potential difference across the capacitor is
the same as the potential difference across V2, which is the battery’s terminal voltage (not its emf). Start at
junction c on the right side of battery V2 and add voltage changes from junction c to junction b on the left
side of the battery:
c 2 b b c b c
12 2 ; 12 2 1.11 ; 9.78 V
This is the potential difference across the capacitor: 9.78 V
The charge stored on the capacitor is
: 10.0 F 9.78 V ; 97.8 C (10 points)
V I V V V V V
V
q CV q q
2. a.
0
Loop Rule: 0 0 or 0
IC: 0 (10 points)
q q dq q
iR i
C RC dt RC
qq
b.
00
1 1 1
From part a: ; ; ln ln
(where is a constant). Then . When 0, so that .
tt
RC RC
dq dq
dt dt q t k
q RC q RC RC
k q ke t q q q q e
(12 points)
The negative answer for
I1 indicates that this
loop current flows
opposite to the direction
assumed. (3 points)
I2
